From 092d8a3726fd07adbe20a67026cf5aba858c1266 Mon Sep 17 00:00:00 2001
From: Ping He <phe@iastate.edu>
Date: Sat, 19 Jun 2021 14:46:05 -0400
Subject: [PATCH] Time accurate adjoint (#152)

* Changed the objFuncHist filename to objFuncTimeSeries to avoid confusion.

* Changed the hybridAdjoint flag such that it will not save states when inactive.

* Added an option to save intermediate variables for time-accurate adjoint.

* Added the dt residual terms and also fixed the missing ddtCorr terms for pisoFoam.

* Checked if both hybrid and time-accurate adjoints are active.

* Updated pisoFoam tests

* Added mesh.moving(false) right after mesh.movePoints() calls.

* Updated tests.

* Assigned fields and their oldTime(). Adjoint residual matched flow.

* Removed the time and timeIndex lists.

* Reverted back the time list.

* The time accurate residual worked for JacobianFree.

* Fixed the issue that the initial residual (ddt part) in the AD code is not correctly computed.

* Assigned all oldTimes even a variable does not need them.

* Added the calculation of dRdWOldTPsi using AD.

* Implemented the off-diagonal block terms. Also fixed a problem for first two step residuals. The last step residual is still not quite right.

* Updated the residual for pisoFoam with ts.

* Moved the unsteady adjoint functions from PisoFoam to DASolver.

* Updated tests.

* Added DAPimpleFoam primal.

* Added residual computation for pimpleFoam.

* Added the initOldTimes function to fix the issue that the first setTimeInstance call could not set the correct oldTime field.

* Updated the unsteadyAdjoint option.

* Reverted the adjoint calling sequence for hybridAdjoint.

* Updated test.

* Fixed an issue in assigning dRdWOldTPsi. Added zero timeAccurateVecs function.

* Fixed an issue for computing mean field.

* Fixed an issue for oldTime derivative by not registering oldTime fields if we do not need them in residual computation. Not doing this will get completely off adjoint derivative, especially for the calcdRdWTOldPsi function.

* Added the DALaplacianFoam solver.

* Removed all ResPartDeriv variables because they are not used.

* Fixed the missing part in solid MakeFiles.

* Added DAScalarTransportFoam.

* Fixed bugs for Laplacian and ScalarTransportFoam. Derivs not accurate.

* Fixed a bug in the actuatorDisk and actuatorLine models that impacted their circ force computation.

* Fixed a bug in the fCirc calculation for actuators to make the profile more smooth.

* Fixed a minor issue.

* Updated the tests.

* Relaxed the test tolerance.

* Changed the version to 226
---
 dafoam/optFuncs.py                            |  43 +-
 dafoam/pyDAFoam.py                            | 184 ++++-
 src/adjoint/DAField/DAField.C                 | 222 ++++--
 src/adjoint/DAField/DAField.H                 |   3 +-
 .../DAFvSource/DAFvSourceActuatorDisk.C       |  31 +-
 .../DAFvSource/DAFvSourceActuatorLine.C       |  23 +-
 src/adjoint/DAIndex/DAIndex.C                 |   4 +
 src/adjoint/DAIntmdVar/DAIntmdVar.C           |  18 +-
 .../DATurbulenceModel/DASpalartAllmaras.C     |   8 -
 .../DATurbulenceModel/DASpalartAllmaras.H     |   1 -
 .../DATurbulenceModel/DASpalartAllmarasFv3.C  |   8 -
 .../DATurbulenceModel/DASpalartAllmarasFv3.H  |   1 -
 .../DASpalartAllmarasFv3Beta.C                |   8 -
 .../DASpalartAllmarasFv3Beta.H                |   1 -
 .../DAModel/DATurbulenceModel/DAkOmega.C      |  18 +-
 .../DAModel/DATurbulenceModel/DAkOmega.H      |   2 -
 .../DAModel/DATurbulenceModel/DAkOmegaSST.C   |  16 -
 .../DAModel/DATurbulenceModel/DAkOmegaSST.H   |   2 -
 .../DAModel/DATurbulenceModel/DAkOmegaSSTLM.C |  32 -
 .../DAModel/DATurbulenceModel/DAkOmegaSSTLM.H |   4 -
 .../DAResidual/DAResidualLaplacianFoam.C      | 102 +++
 .../DAResidual/DAResidualLaplacianFoam.H      |  79 +++
 src/adjoint/DAResidual/DAResidualPimpleFoam.C | 194 ++++++
 src/adjoint/DAResidual/DAResidualPimpleFoam.H |  99 +++
 src/adjoint/DAResidual/DAResidualPisoFoam.C   |  26 +-
 src/adjoint/DAResidual/DAResidualPisoFoam.H   |   6 +-
 .../DAResidual/DAResidualRhoSimpleCFoam.C     |   4 -
 .../DAResidual/DAResidualRhoSimpleCFoam.H     |   4 -
 .../DAResidual/DAResidualRhoSimpleFoam.C      |   4 -
 .../DAResidual/DAResidualRhoSimpleFoam.H      |   4 -
 .../DAResidualScalarTransportFoam.C           | 107 +++
 .../DAResidualScalarTransportFoam.H           |  80 +++
 src/adjoint/DAResidual/DAResidualSimpleFoam.C |   3 -
 src/adjoint/DAResidual/DAResidualSimpleFoam.H |   3 -
 .../DAResidual/DAResidualSimpleTFoam.C        |   4 -
 .../DAResidual/DAResidualSimpleTFoam.H        |   4 -
 .../DAResidualSolidDisplacementFoam.C         |   1 -
 .../DAResidualSolidDisplacementFoam.H         |   1 -
 src/adjoint/DAResidual/DAResidualTurboFoam.C  |   4 -
 src/adjoint/DAResidual/DAResidualTurboFoam.H  |   4 -
 .../DALaplacianFoam/DALaplacianFoam.C         | 229 ++++++
 .../DALaplacianFoam/DALaplacianFoam.H         |  76 ++
 .../DALaplacianFoam/createFieldsLaplacian.H   |  31 +
 .../DALaplacianFoam/createRefsLaplacian.H     |  11 +
 .../DASolver/DAPimpleFoam/DAPimpleFoam.C      | 264 +++++++
 .../DASolver/DAPimpleFoam/DAPimpleFoam.H      | 114 +++
 .../DASolver/DAPimpleFoam/UEqnPimple.H        |  26 +
 .../DAPimpleFoam/createFieldsPimple.H         |  52 ++
 .../DASolver/DAPimpleFoam/createRefsPimple.H  |  18 +
 .../DASolver/DAPimpleFoam/pEqnPimple.H        |  55 ++
 src/adjoint/DASolver/DAPisoFoam/DAPisoFoam.C  | 182 ++---
 src/adjoint/DASolver/DAPisoFoam/DAPisoFoam.H  |  35 +-
 .../DASolver/DAPisoFoam/createRefsPiso.H      |   2 +-
 src/adjoint/DASolver/DAPisoFoam/pEqnPiso.H    |   5 +-
 .../DARhoSimpleCFoam/createRefsRhoSimpleC.H   |   2 +-
 .../DARhoSimpleFoam/createRefsRhoSimple.H     |   2 +-
 .../DAScalarTransportFoam.C                   | 234 +++++++
 .../DAScalarTransportFoam.H                   |  82 +++
 .../createFieldsScalarTransport.H             |  58 ++
 .../createRefsScalarTransport.H               |  12 +
 .../DASolver/DASimpleFoam/createRefsSimple.H  |   2 +-
 .../DASimpleTFoam/createRefsSimpleT.H         |   2 +-
 .../createRefsSolidDisplacement.H             |   2 +-
 src/adjoint/DASolver/DASolver.C               | 653 ++++++++++++++++--
 src/adjoint/DASolver/DASolver.H               |  60 +-
 .../DASolver/DATurboFoam/createRefsTurbo.H    |   2 +-
 .../DAStateInfo/DAStateInfoLaplacianFoam.C    |  81 +++
 .../DAStateInfo/DAStateInfoLaplacianFoam.H    |  55 ++
 .../DAStateInfo/DAStateInfoPimpleFoam.C       | 116 ++++
 .../DAStateInfo/DAStateInfoPimpleFoam.H       |  55 ++
 .../DAStateInfoScalarTransportFoam.C          |  81 +++
 .../DAStateInfoScalarTransportFoam.H          |  55 ++
 src/adjoint/Make/files_Incompressible         |   5 +-
 src/adjoint/Make/files_Solid                  |   9 +
 src/include/DAMacroFunctions.H                |  35 +-
 src/include/createPimpleControlPython.H       |  14 +
 src/pyDASolvers/DASolvers.H                   |  38 +
 src/pyDASolvers/pyDASolvers.pyx               |  20 +
 tests/refs/DAFoam_Test_DAPisoFoamACTLRef.txt  |  66 +-
 tests/refs/DAFoam_Test_DAPisoFoamRef.txt      |  58 +-
 .../DAFoam_Test_DARhoSimpleCFoamADRef.txt     |  18 +-
 .../refs/DAFoam_Test_DARhoSimpleCFoamRef.txt  |  18 +-
 .../refs/DAFoam_Test_DARhoSimpleFoamADRef.txt | 152 ++--
 .../DAFoam_Test_DARhoSimpleFoamMRFRef.txt     |  18 +-
 tests/refs/DAFoam_Test_DARhoSimpleFoamRef.txt |  26 +-
 .../DAFoam_Test_DARhoSimpleFoamUBendRef.txt   |  26 +-
 tests/refs/DAFoam_Test_DASimpleFoamADRef.txt  |  18 +-
 tests/refs/DAFoam_Test_DASimpleFoamMRFRef.txt |  18 +-
 tests/refs/DAFoam_Test_DASimpleFoamRef.txt    | 140 ++--
 tests/refs/DAFoam_Test_DASimpleTFoamRef.txt   |  26 +-
 ...DAFoam_Test_DASolidDisplacementFoamRef.txt |  26 +-
 .../DAFoam_Test_DATurboFoamSubsonicRef.txt    |  34 +-
 .../DAFoam_Test_DATurboFoamTransonicRef.txt   |  66 +-
 tests/refs/DAFoam_Test_IntegrationRef.txt     |  42 +-
 tests/runTests_DAPisoFoam.py                  |  20 +-
 tests/runTests_DAPisoFoamACTL.py              |  20 +-
 tests/runTests_DARhoSimpleCFoam.py            |   2 +-
 tests/runTests_DARhoSimpleCFoamAD.py          |   2 +-
 tests/runTests_DARhoSimpleFoam.py             |   2 +-
 tests/runTests_DARhoSimpleFoamAD.py           |   6 +-
 tests/runTests_DARhoSimpleFoamMRF.py          |   2 +-
 tests/runTests_DARhoSimpleFoamUBend.py        |   2 +-
 tests/runTests_DASimpleFoam.py                |   4 +-
 tests/runTests_DASimpleFoamAD.py              |   2 +-
 tests/runTests_DASimpleFoamMRF.py             |   2 +-
 tests/runTests_DASimpleTFoam.py               |   2 +-
 tests/runTests_DASolidDisplacementFoam.py     |   2 +-
 tests/runTests_DATurboFoamSubsonic.py         |   2 +-
 tests/runTests_DATurboFoamTransonic.py        |   2 +-
 109 files changed, 4052 insertions(+), 909 deletions(-)
 create mode 100755 src/adjoint/DAResidual/DAResidualLaplacianFoam.C
 create mode 100755 src/adjoint/DAResidual/DAResidualLaplacianFoam.H
 create mode 100755 src/adjoint/DAResidual/DAResidualPimpleFoam.C
 create mode 100755 src/adjoint/DAResidual/DAResidualPimpleFoam.H
 create mode 100755 src/adjoint/DAResidual/DAResidualScalarTransportFoam.C
 create mode 100755 src/adjoint/DAResidual/DAResidualScalarTransportFoam.H
 create mode 100755 src/adjoint/DASolver/DALaplacianFoam/DALaplacianFoam.C
 create mode 100755 src/adjoint/DASolver/DALaplacianFoam/DALaplacianFoam.H
 create mode 100755 src/adjoint/DASolver/DALaplacianFoam/createFieldsLaplacian.H
 create mode 100755 src/adjoint/DASolver/DALaplacianFoam/createRefsLaplacian.H
 create mode 100755 src/adjoint/DASolver/DAPimpleFoam/DAPimpleFoam.C
 create mode 100755 src/adjoint/DASolver/DAPimpleFoam/DAPimpleFoam.H
 create mode 100755 src/adjoint/DASolver/DAPimpleFoam/UEqnPimple.H
 create mode 100755 src/adjoint/DASolver/DAPimpleFoam/createFieldsPimple.H
 create mode 100755 src/adjoint/DASolver/DAPimpleFoam/createRefsPimple.H
 create mode 100755 src/adjoint/DASolver/DAPimpleFoam/pEqnPimple.H
 create mode 100755 src/adjoint/DASolver/DAScalarTransportFoam/DAScalarTransportFoam.C
 create mode 100755 src/adjoint/DASolver/DAScalarTransportFoam/DAScalarTransportFoam.H
 create mode 100755 src/adjoint/DASolver/DAScalarTransportFoam/createFieldsScalarTransport.H
 create mode 100755 src/adjoint/DASolver/DAScalarTransportFoam/createRefsScalarTransport.H
 create mode 100755 src/adjoint/DAStateInfo/DAStateInfoLaplacianFoam.C
 create mode 100755 src/adjoint/DAStateInfo/DAStateInfoLaplacianFoam.H
 create mode 100755 src/adjoint/DAStateInfo/DAStateInfoPimpleFoam.C
 create mode 100755 src/adjoint/DAStateInfo/DAStateInfoPimpleFoam.H
 create mode 100755 src/adjoint/DAStateInfo/DAStateInfoScalarTransportFoam.C
 create mode 100755 src/adjoint/DAStateInfo/DAStateInfoScalarTransportFoam.H
 create mode 100755 src/include/createPimpleControlPython.H

diff --git a/dafoam/optFuncs.py b/dafoam/optFuncs.py
index ffd2088a..57c2da02 100755
--- a/dafoam/optFuncs.py
+++ b/dafoam/optFuncs.py
@@ -136,10 +136,10 @@ def calcObjFuncValuesMP(xDV):
     return funcsMP, fail
 
 
-def calcObjFuncValuesHybridAdjoint(xDV):
+def calcObjFuncValuesUnsteady(xDV):
     """
     Update the design surface and run the primal solver to get objective function values.
-    This is the hybrid adjoint version of calcObjFuncValues
+    This is the unsteady adjoint version of calcObjFuncValues
     """
 
     Info("\n")
@@ -164,9 +164,12 @@ def calcObjFuncValuesHybridAdjoint(xDV):
     # Solve the CFD problem
     DASolver()
 
-    # Set values for the hybrid adjoint objectives. This function needs to be
+    # Set values for the unsteady adjoint objectives. This function needs to be
     # implemented in run scripts
-    setHybridAdjointObjFuncs(DASolver, funcs, evalFuncs)
+    setObjFuncsUnsteady(DASolver, funcs, evalFuncs)
+
+    # assign state lists to mats
+    DASolver.setTimeInstanceVar(mode="list2Mat")
 
     b = time.time()
 
@@ -217,7 +220,7 @@ def calcObjFuncSens(xDV, funcs):
         Info("Objective Function Sensitivity: ")
         Info(funcsSens)
         Info("Adjoint Runtime: %g s" % (b - a))
-    
+
     # write the sensitivity values to file
     DASolver.writeTotalDeriv("totalDerivHist.txt", funcsSens, evalFuncs)
 
@@ -299,10 +302,10 @@ def calcObjFuncSensMP(xDV, funcs):
     return funcsSensMP, fail
 
 
-def calcObjFuncSensHybridAdjoint(xDV, funcs):
+def calcObjFuncSensUnsteady(xDV, funcs):
     """
     Run the adjoint solver and get objective function sensitivities.
-    This is the hybrid adjoint version of calcObjFuncSens
+    This is the unsteady adjoint version of calcObjFuncSens
     """
 
     Info("\n")
@@ -320,14 +323,32 @@ def calcObjFuncSensHybridAdjoint(xDV, funcs):
     # write the deform FFDs
     DASolver.writeDeformedFFDs()
 
+    # assign the state mats to lists
+    DASolver.setTimeInstanceVar(mode="mat2List")
+
     # Setup an empty dictionary for the evaluated derivative values
     funcsSensCombined = {}
 
     funcsSensAllInstances = []
 
-    nTimeInstances = DASolver.getOption("hybridAdjoint")["nTimeInstances"]
+    mode = DASolver.getOption("unsteadyAdjoint")["mode"]
+    nTimeInstances = DASolver.getOption("unsteadyAdjoint")["nTimeInstances"]
+    if mode == "hybridAdjoint":
+        iEnd = -1
+    elif mode == "timeAccurateAdjoint":
+        iEnd = 0
+
+    # NOTE: calling calcRes here is critical because it will setup the correct
+    # old time levels for setTimeInstanceField. Otherwise, the residual for the
+    # first adjoint time instance will be incorrect because the residuals have
+    # not been computed and the old time levels will be zeros for all variables,
+    # this will create issues for the setTimeInstanceField call (nOldTimes)
+    DASolver.calcPrimalResidualStatistics("calc")
+
+    # set these vectors zeros
+    DASolver.zeroTimeAccurateAdjointVectors()
 
-    for i in range(nTimeInstances):
+    for i in range(nTimeInstances - 1, iEnd, -1):
 
         Info("--Solving Adjoint for Time Instance %d--" % i)
 
@@ -355,13 +376,13 @@ def calcObjFuncSensHybridAdjoint(xDV, funcs):
 
         funcsSensAllInstances.append(funcsSens)
 
-    setHybridAdjointObjFuncsSens(DASolver, funcs, funcsSensAllInstances, funcsSensCombined)
+    setObjFuncsSensUnsteady(DASolver, funcs, funcsSensAllInstances, funcsSensCombined)
 
     funcsSensCombined["fail"] = fail
 
     # Print the current solution to the screen
     with np.printoptions(precision=16, threshold=5, suppress=True):
-        Info("Objective Function Sensitivity Hybrid Adjoint: ")
+        Info("Objective Function Sensitivity Unsteady Adjoint: ")
         Info(funcsSensCombined)
 
     b = time.time()
diff --git a/dafoam/pyDAFoam.py b/dafoam/pyDAFoam.py
index e8d40fcd..01efe1c1 100755
--- a/dafoam/pyDAFoam.py
+++ b/dafoam/pyDAFoam.py
@@ -11,7 +11,7 @@
 
 """
 
-__version__ = "2.2.5"
+__version__ = "2.2.6"
 
 import subprocess
 import os
@@ -57,6 +57,7 @@ class DAOPTION(object):
     ## - DASimpleFoam:            Incompressible steady-state flow solver for Navier-Stokes equations
     ## - DASimpleTFoam:           Incompressible steady-state flow solver for Navier-Stokes equations with temperature
     ## - DAPisoFoam:              Incompressible transient flow solver for Navier-Stokes equations
+    ## - DAPimpleFoam:            Incompressible transient flow solver for Navier-Stokes equations
     ## - DARhoSimpleFoam:         Compressible steady-state flow solver for Navier-Stokes equations (subsonic)
     ## - DARhoSimpleCFoam:        Compressible steady-state flow solver for Navier-Stokes equations (transonic)
     ## - DATurboFoam:             Compressible steady-state flow solver for Navier-Stokes equations (turbomachinery)
@@ -228,6 +229,20 @@ class DAOPTION(object):
     ##                "addToAdjoint": True,
     ##            }
     ##        },
+    ##        "THRUST": {
+    ##            "part1": {
+    ##                "type": "variableVolSum",
+    ##                "source": "boxToCell",
+    ##                "min": [-50.0, -50.0, -50.0],
+    ##                "max": [50.0, 50.0, 50.0],
+    ##                "varName": "fvSource",
+    ##                "varType": "vector",
+    ##                "component": 0,
+    ##                "isSquare": 0,
+    ##                "scale": 1.0,
+    ##                "addToAdjoint": True,
+    ##            },
+    ##        },
     ##        "FI": {
     ##            "part1": {
     ##                "type": "stateErrorNorm",
@@ -397,9 +412,10 @@ class DAOPTION(object):
     ## This is used only for transonic solvers such as DARhoSimpleCFoam
     transonicPCOption = -1
 
-    ## Options for hybrid adjoint. Here nTimeInstances is the number of time instances
-    ## periodicity is the periodicity of flow oscillation
-    hybridAdjoint = {"active": False, "nTimeInstances": -1, "periodicity": -1.0}
+    ## Options for unsteady adjoint. mode can be hybridAdjoint or timeAccurateAdjoint
+    ## Here nTimeInstances is the number of time instances and periodicity is the 
+    ## periodicity of flow oscillation (hybrid adjoint only)
+    unsteadyAdjoint = {"mode": "None", "nTimeInstances": -1, "periodicity": -1.0}
 
     ## At which iteration should we start the averaging of objective functions.
     ## This is only used for unsteady solvers
@@ -703,6 +719,12 @@ def __init__(self, comm=None, options=None):
         # initialize the adjoint vector dict
         self.adjVectors = self._initializeAdjVectors()
 
+        # initialize the dRdWOldTPsi vectors
+        self._initializeTimeAccurateAdjointVectors()
+
+        # check if the combination of options is valid.
+        self._checkOptions()
+
         Info("pyDAFoam initialization done!")
 
         return
@@ -714,9 +736,9 @@ def _solverRegistry(self):
         """
 
         self.solverRegistry = {
-            "Incompressible": ["DASimpleFoam", "DASimpleTFoam", "DAPisoFoam"],
+            "Incompressible": ["DASimpleFoam", "DASimpleTFoam", "DAPisoFoam", "DAPimpleFoam"],
             "Compressible": ["DARhoSimpleFoam", "DARhoSimpleCFoam", "DATurboFoam"],
-            "Solid": ["DASolidDisplacementFoam"],
+            "Solid": ["DASolidDisplacementFoam", "DALaplacianFoam", "DAScalarTransportFoam"],
         }
 
     def __call__(self):
@@ -831,6 +853,62 @@ def _initializeAdjTotalDeriv(self):
 
         return adjTotalDeriv
 
+    def _initializeTimeAccurateAdjointVectors(self):
+        """
+        Initialize the dRdWTPsi vectors for time accurate adjoint.
+        Here we need to initialize current time step and two previous
+        time steps 0 and 00 for both state and residuals. This is
+        because the backward ddt scheme depends on U, U0, and U00
+        """
+        if self.getOption("unsteadyAdjoint")["mode"] == "timeAccurateAdjoint":
+            objFuncDict = self.getOption("objFunc")
+            wSize = self.solver.getNLocalAdjointStates()
+            self.dRdW0TPsi = {}
+            self.dRdW00TPsi = {}
+            self.dR0dW0TPsi = {}
+            self.dR0dW00TPsi = {}
+            self.dR00dW0TPsi = {}
+            self.dR00dW00TPsi = {}
+            for objFuncName in objFuncDict:
+                if objFuncName in self.objFuncNames4Adj:
+                    vecA = PETSc.Vec().create(PETSc.COMM_WORLD)
+                    vecA.setSizes((wSize, PETSc.DECIDE), bsize=1)
+                    vecA.setFromOptions()
+                    vecA.zeroEntries()
+                    self.dRdW0TPsi[objFuncName] = vecA
+
+                    vecB = vecA.duplicate()
+                    vecB.zeroEntries()
+                    self.dRdW00TPsi[objFuncName] = vecB
+
+                    vecC = vecA.duplicate()
+                    vecC.zeroEntries()
+                    self.dR0dW0TPsi[objFuncName] = vecC
+
+                    vecD = vecA.duplicate()
+                    vecD.zeroEntries()
+                    self.dR0dW00TPsi[objFuncName] = vecD
+
+                    vecE = vecA.duplicate()
+                    vecE.zeroEntries()
+                    self.dR00dW0TPsi[objFuncName] = vecE
+
+                    vecF = vecA.duplicate()
+                    vecF.zeroEntries()
+                    self.dR00dW00TPsi[objFuncName] = vecF
+    
+    def zeroTimeAccurateAdjointVectors(self):
+        if self.getOption("unsteadyAdjoint")["mode"] == "timeAccurateAdjoint":
+            objFuncDict = self.getOption("objFunc")
+            for objFuncName in objFuncDict:
+                if objFuncName in self.objFuncNames4Adj:
+                    self.dRdW0TPsi[objFuncName].zeroEntries()
+                    self.dRdW00TPsi[objFuncName].zeroEntries()
+                    self.dR0dW0TPsi[objFuncName].zeroEntries()
+                    self.dR0dW00TPsi[objFuncName].zeroEntries()
+                    self.dR00dW0TPsi[objFuncName].zeroEntries()
+                    self.dR00dW00TPsi[objFuncName].zeroEntries()
+
     def _calcObjFuncNames4Adj(self):
         """
         Compute the objective function names for which we solve the adjoint equation
@@ -857,6 +935,20 @@ def _calcObjFuncNames4Adj(self):
                     raise Error("addToAdjoint can be either True or False")
         return objFuncList
 
+    def _checkOptions(self):
+        """
+        Check if the combination of options are valid.
+        For example, if timeAccurateAdjoint is active, we have to set
+        adjJacobianOption = JacobianFree
+        NOTE: we should add all possible checks here!
+        """
+        # check time accurate adjoint
+        if self.getOption("unsteadyAdjoint")["mode"] == "timeAccurateAdjoint":
+            if not self.getOption("adjJacobianOption") == "JacobianFree":
+                raise Error("timeAccurateAdjoint only supports adjJacobianOption=JacobianFree!")
+
+        # check other combinations...
+
     def saveMultiPointField(self, indexMP):
         """
         Save the state variable vector to self.wVecMPList
@@ -885,18 +977,76 @@ def setMultiPointField(self, indexMP):
 
         return
 
+    def calcPrimalResidualStatistics(self, mode):
+        if self.getOption("adjJacobianOption") == "JacobianFD":
+            self.solver.calcPrimalResidualStatistics(mode.encode())
+        elif self.getOption("adjJacobianOption") == "JacobianFree":
+            self.solverAD.calcPrimalResidualStatistics(mode.encode())
+
     def setTimeInstanceField(self, instanceI):
         """
         Set the OpenFOAM state variables based on instance index
         """
 
-        self.solver.setTimeInstanceField(instanceI)
+        if self.getOption("adjJacobianOption") == "JacobianFD":
+            solver = self.solver
+        elif self.getOption("adjJacobianOption") == "JacobianFree":
+            solver = self.solverAD
+
+        solver.setTimeInstanceField(instanceI)
         # NOTE: we need to set the OF field to wVec vector here!
         # this is because we will assign self.wVec to the solveAdjoint function later
-        self.solver.ofField2StateVec(self.wVec)
+        solver.ofField2StateVec(self.wVec)
 
         return
 
+    def initTimeInstanceMats(self):
+
+        nLocalAdjointStates = self.solver.getNLocalAdjointStates()
+        nLocalAdjointBoundaryStates = self.solver.getNLocalAdjointBoundaryStates()
+        nTimeInstances = -99999
+        adjMode = self.getOption("unsteadyAdjoint")["mode"]
+        if adjMode == "hybridAdjoint" or adjMode == "timeAccurateAdjoint":
+            nTimeInstances = self.getOption("unsteadyAdjoint")["nTimeInstances"]
+
+        self.stateMat = PETSc.Mat().create(PETSc.COMM_WORLD)
+        self.stateMat.setSizes(((nLocalAdjointStates, None), (None, nTimeInstances)))
+        self.stateMat.setFromOptions()
+        self.stateMat.setPreallocationNNZ((nTimeInstances, nTimeInstances))
+        self.stateMat.setUp()
+
+        self.stateBCMat = PETSc.Mat().create(PETSc.COMM_WORLD)
+        self.stateBCMat.setSizes(((nLocalAdjointBoundaryStates, None), (None, nTimeInstances)))
+        self.stateBCMat.setFromOptions()
+        self.stateBCMat.setPreallocationNNZ((nTimeInstances, nTimeInstances))
+        self.stateBCMat.setUp()
+
+        self.timeVec = PETSc.Vec().createSeq(nTimeInstances, bsize=1, comm=PETSc.COMM_SELF)
+        self.timeIdxVec = PETSc.Vec().createSeq(nTimeInstances, bsize=1, comm=PETSc.COMM_SELF)
+    
+    def initOldTimes(self):
+        # No need to initialize oldTimes for FD
+        if self.getOption("adjJacobianOption") == "JacobianFree":
+            self.solverAD.initOldTimes()
+
+    def setTimeInstanceVar(self, mode):
+
+        if mode == "list2Mat":
+            self.solver.setTimeInstanceVar(mode.encode(), self.stateMat, self.stateBCMat, self.timeVec, self.timeIdxVec)
+        elif mode == "mat2List":
+            if self.getOption("adjJacobianOption") == "JacobianFD":
+                self.solver.setTimeInstanceVar(
+                    mode.encode(), self.stateMat, self.stateBCMat, self.timeVec, self.timeIdxVec
+                )
+            elif self.getOption("adjJacobianOption") == "JacobianFree":
+                self.solverAD.setTimeInstanceVar(
+                    mode.encode(), self.stateMat, self.stateBCMat, self.timeVec, self.timeIdxVec
+                )
+            else:
+                raise Error("adjJacobianOption can only be either JacobianFD or JacobianFree!")
+        else:
+            raise Error("mode can only be either mat2List or list2Mat!")
+
     def writeDesignVariable(self, fileName, xDV):
         """
         Write the design variable history to files in the json format
@@ -1703,12 +1853,26 @@ def solveAdjoint(self):
                 elif self.getOption("adjJacobianOption") == "JacobianFree":
                     self.solverAD.calcdFdWAD(self.xvVec, self.wVec, objFuncName.encode(), dFdW)
 
+                # if it is time accurate adjoint, add extra terms for dFdW
+                if self.getOption("unsteadyAdjoint")["mode"] == "timeAccurateAdjoint":
+                    # first copy the vectors from previous residual time step level
+                    self.dR0dW0TPsi[objFuncName].copy(self.dR00dW0TPsi[objFuncName])
+                    self.dR0dW00TPsi[objFuncName].copy(self.dR00dW00TPsi[objFuncName])
+                    self.dRdW0TPsi[objFuncName].copy(self.dR0dW0TPsi[objFuncName])
+                    self.dRdW00TPsi[objFuncName].copy(self.dR0dW00TPsi[objFuncName])
+                    dFdW.axpy(-1.0, self.dR0dW0TPsi[objFuncName])
+                    dFdW.axpy(-1.0, self.dR00dW00TPsi[objFuncName])
+
                 # Initialize the adjoint vector psi and solve for it
                 if self.getOption("adjJacobianOption") == "JacobianFD":
                     self.adjointFail = self.solver.solveLinearEqn(ksp, dFdW, self.adjVectors[objFuncName])
                 elif self.getOption("adjJacobianOption") == "JacobianFree":
                     self.adjointFail = self.solverAD.solveLinearEqn(ksp, dFdW, self.adjVectors[objFuncName])
 
+                if self.getOption("unsteadyAdjoint")["mode"] == "timeAccurateAdjoint":
+                    self.solverAD.calcdRdWOldTPsiAD(1, self.adjVectors[objFuncName], self.dRdW0TPsi[objFuncName])
+                    self.solverAD.calcdRdWOldTPsiAD(2, self.adjVectors[objFuncName], self.dRdW00TPsi[objFuncName])
+
                 dFdW.destroy()
 
         ksp.destroy()
@@ -2206,6 +2370,10 @@ def _initSolver(self):
         if self.getOption("printDAOptions"):
             self.solver.printAllOptions()
 
+        adjMode = self.getOption("unsteadyAdjoint")["mode"]
+        if adjMode == "hybridAdjoint" or adjMode == "timeAccurateAdjoint":
+            self.initTimeInstanceMats()
+
         self.solverInitialized = 1
 
         return
diff --git a/src/adjoint/DAField/DAField.C b/src/adjoint/DAField/DAField.C
index c15fbd5c..eb2d5f2d 100755
--- a/src/adjoint/DAField/DAField.C
+++ b/src/adjoint/DAField/DAField.C
@@ -256,6 +256,7 @@ void DAField::pointVec2OFMesh(const Vec xvVec) const
     // movePoints update the mesh metrics such as volume, surface area and cell centers
     fvMesh& mesh = const_cast<fvMesh&>(mesh_);
     mesh.movePoints(meshPoints);
+    mesh.moving(false);
 }
 
 void DAField::ofMesh2PointVec(Vec xvVec) const
@@ -1161,7 +1162,8 @@ void DAField::ofField2List(
 
 void DAField::list2OFField(
     const scalarList& stateList,
-    const scalarList& stateBoundaryList) const
+    const scalarList& stateBoundaryList,
+    const label oldTimeLevel) const
 {
     /*
     Description:
@@ -1170,6 +1172,8 @@ void DAField::list2OFField(
     Input:
     stateList: scalar list of states
     stateBoundaryList: scalar list of boundary states
+    oldTimeLevel: assign to oldTime field instead of the original field, this will
+      be used in time-accurate adjoint
 
     Output:
     OpenFoam field variables
@@ -1188,30 +1192,66 @@ void DAField::list2OFField(
 
     label localBFaceI = 0;
 
+    if (oldTimeLevel > 2 || oldTimeLevel < 0)
+    {
+        FatalErrorIn("") << "oldTimeLevel not valid!"
+                         << abort(FatalError);
+    }
+
     forAll(stateInfo_["volVectorStates"], idxI)
     {
         // lookup state from meshDb
         makeState(stateInfo_["volVectorStates"][idxI], volVectorField, db);
 
-        forAll(mesh_.cells(), cellI)
+        label maxOldTimes = state.nOldTimes();
+
+        if (maxOldTimes >= oldTimeLevel)
         {
-            for (label comp = 0; comp < 3; comp++)
+            forAll(mesh_.cells(), cellI)
             {
-                label localIdx = daIndex_.getLocalAdjointStateIndex(stateName, cellI, comp);
-                state[cellI][comp] = stateList[localIdx];
+                for (label comp = 0; comp < 3; comp++)
+                {
+                    label localIdx = daIndex_.getLocalAdjointStateIndex(stateName, cellI, comp);
+                    if (oldTimeLevel == 0)
+                    {
+                        state[cellI][comp] = stateList[localIdx];
+                    }
+                    else if (oldTimeLevel == 1)
+                    {
+                        state.oldTime()[cellI][comp] = stateList[localIdx];
+                    }
+                    else if (oldTimeLevel == 2)
+                    {
+                        state.oldTime().oldTime()[cellI][comp] = stateList[localIdx];
+                    }
+                }
             }
-        }
 
-        forAll(state.boundaryField(), patchI)
-        {
-            if (state.boundaryField()[patchI].size() > 0)
+            forAll(state.boundaryField(), patchI)
             {
-                forAll(state.boundaryField()[patchI], faceI)
+                if (state.boundaryField()[patchI].size() > 0)
                 {
-                    for (label comp = 0; comp < 3; comp++)
+                    forAll(state.boundaryField()[patchI], faceI)
                     {
-                        state.boundaryFieldRef()[patchI][faceI][comp] = stateBoundaryList[localBFaceI];
-                        localBFaceI++;
+                        for (label comp = 0; comp < 3; comp++)
+                        {
+                            if (oldTimeLevel == 0)
+                            {
+                                state.boundaryFieldRef()[patchI][faceI][comp] =
+                                    stateBoundaryList[localBFaceI];
+                            }
+                            else if (oldTimeLevel == 1)
+                            {
+                                state.oldTime().boundaryFieldRef()[patchI][faceI][comp] =
+                                    stateBoundaryList[localBFaceI];
+                            }
+                            else if (oldTimeLevel == 2)
+                            {
+                                state.oldTime().oldTime().boundaryFieldRef()[patchI][faceI][comp] =
+                                    stateBoundaryList[localBFaceI];
+                            }
+                            localBFaceI++;
+                        }
                     }
                 }
             }
@@ -1223,20 +1263,51 @@ void DAField::list2OFField(
         // lookup state from meshDb
         makeState(stateInfo_["volScalarStates"][idxI], volScalarField, db);
 
-        forAll(mesh_.cells(), cellI)
-        {
-            label localIdx = daIndex_.getLocalAdjointStateIndex(stateName, cellI);
-            state[cellI] = stateList[localIdx];
-        }
+        label maxOldTimes = state.nOldTimes();
 
-        forAll(state.boundaryField(), patchI)
+        if (maxOldTimes >= oldTimeLevel)
         {
-            if (state.boundaryField()[patchI].size() > 0)
+
+            forAll(mesh_.cells(), cellI)
             {
-                forAll(state.boundaryField()[patchI], faceI)
+                label localIdx = daIndex_.getLocalAdjointStateIndex(stateName, cellI);
+                if (oldTimeLevel == 0)
                 {
-                    state.boundaryFieldRef()[patchI][faceI] = stateBoundaryList[localBFaceI];
-                    localBFaceI++;
+                    state[cellI] = stateList[localIdx];
+                }
+                else if (oldTimeLevel == 1)
+                {
+                    state.oldTime()[cellI] = stateList[localIdx];
+                }
+                else if (oldTimeLevel == 2)
+                {
+                    state.oldTime().oldTime()[cellI] = stateList[localIdx];
+                }
+            }
+
+            forAll(state.boundaryField(), patchI)
+            {
+                if (state.boundaryField()[patchI].size() > 0)
+                {
+                    forAll(state.boundaryField()[patchI], faceI)
+                    {
+                        if (oldTimeLevel == 0)
+                        {
+                            state.boundaryFieldRef()[patchI][faceI] =
+                                stateBoundaryList[localBFaceI];
+                        }
+                        else if (oldTimeLevel == 1)
+                        {
+                            state.oldTime().boundaryFieldRef()[patchI][faceI] =
+                                stateBoundaryList[localBFaceI];
+                        }
+                        else if (oldTimeLevel == 2)
+                        {
+                            state.oldTime().oldTime().boundaryFieldRef()[patchI][faceI] =
+                                stateBoundaryList[localBFaceI];
+                        }
+                        localBFaceI++;
+                    }
                 }
             }
         }
@@ -1247,20 +1318,51 @@ void DAField::list2OFField(
         // lookup state from meshDb
         makeState(stateInfo_["modelStates"][idxI], volScalarField, db);
 
-        forAll(mesh_.cells(), cellI)
-        {
-            label localIdx = daIndex_.getLocalAdjointStateIndex(stateName, cellI);
-            state[cellI] = stateList[localIdx];
-        }
+        label maxOldTimes = state.nOldTimes();
 
-        forAll(state.boundaryField(), patchI)
+        if (maxOldTimes >= oldTimeLevel)
         {
-            if (state.boundaryField()[patchI].size() > 0)
+
+            forAll(mesh_.cells(), cellI)
             {
-                forAll(state.boundaryField()[patchI], faceI)
+                label localIdx = daIndex_.getLocalAdjointStateIndex(stateName, cellI);
+                if (oldTimeLevel == 0)
                 {
-                    state.boundaryFieldRef()[patchI][faceI] = stateBoundaryList[localBFaceI];
-                    localBFaceI++;
+                    state[cellI] = stateList[localIdx];
+                }
+                else if (oldTimeLevel == 1)
+                {
+                    state.oldTime()[cellI] = stateList[localIdx];
+                }
+                else if (oldTimeLevel == 2)
+                {
+                    state.oldTime().oldTime()[cellI] = stateList[localIdx];
+                }
+            }
+
+            forAll(state.boundaryField(), patchI)
+            {
+                if (state.boundaryField()[patchI].size() > 0)
+                {
+                    forAll(state.boundaryField()[patchI], faceI)
+                    {
+                        if (oldTimeLevel == 0)
+                        {
+                            state.boundaryFieldRef()[patchI][faceI] =
+                                stateBoundaryList[localBFaceI];
+                        }
+                        else if (oldTimeLevel == 1)
+                        {
+                            state.oldTime().boundaryFieldRef()[patchI][faceI] =
+                                stateBoundaryList[localBFaceI];
+                        }
+                        else if (oldTimeLevel == 2)
+                        {
+                            state.oldTime().oldTime().boundaryFieldRef()[patchI][faceI] =
+                                stateBoundaryList[localBFaceI];
+                        }
+                        localBFaceI++;
+                    }
                 }
             }
         }
@@ -1271,19 +1373,51 @@ void DAField::list2OFField(
         // lookup state from meshDb
         makeState(stateInfo_["surfaceScalarStates"][idxI], surfaceScalarField, db);
 
-        forAll(mesh_.faces(), faceI)
+        label maxOldTimes = state.nOldTimes();
+
+        if (maxOldTimes >= oldTimeLevel)
         {
-            label localIdx = daIndex_.getLocalAdjointStateIndex(stateName, faceI);
-            if (faceI < daIndex_.nLocalInternalFaces)
-            {
-                state[faceI] = stateList[localIdx];
-            }
-            else
+
+            forAll(mesh_.faces(), faceI)
             {
-                label relIdx = faceI - daIndex_.nLocalInternalFaces;
-                const label& patchIdx = daIndex_.bFacePatchI[relIdx];
-                const label& faceIdx = daIndex_.bFaceFaceI[relIdx];
-                state.boundaryFieldRef()[patchIdx][faceIdx] = stateList[localIdx];
+                label localIdx = daIndex_.getLocalAdjointStateIndex(stateName, faceI);
+                if (faceI < daIndex_.nLocalInternalFaces)
+                {
+
+                    if (oldTimeLevel == 0)
+                    {
+                        state[faceI] = stateList[localIdx];
+                    }
+                    else if (oldTimeLevel == 1)
+                    {
+                        state.oldTime()[faceI] = stateList[localIdx];
+                    }
+                    else if (oldTimeLevel == 2)
+                    {
+                        state.oldTime().oldTime()[faceI] = stateList[localIdx];
+                    }
+                }
+                else
+                {
+                    label relIdx = faceI - daIndex_.nLocalInternalFaces;
+                    const label& patchIdx = daIndex_.bFacePatchI[relIdx];
+                    const label& faceIdx = daIndex_.bFaceFaceI[relIdx];
+                    if (oldTimeLevel == 0)
+                    {
+                        state.boundaryFieldRef()[patchIdx][faceIdx] =
+                            stateList[localIdx];
+                    }
+                    else if (oldTimeLevel == 1)
+                    {
+                        state.oldTime().boundaryFieldRef()[patchIdx][faceIdx] =
+                            stateList[localIdx];
+                    }
+                    else if (oldTimeLevel == 2)
+                    {
+                        state.oldTime().oldTime().boundaryFieldRef()[patchIdx][faceIdx] =
+                            stateList[localIdx];
+                    }
+                }
             }
         }
     }
diff --git a/src/adjoint/DAField/DAField.H b/src/adjoint/DAField/DAField.H
index cc14ba7f..659f7966 100755
--- a/src/adjoint/DAField/DAField.H
+++ b/src/adjoint/DAField/DAField.H
@@ -100,7 +100,8 @@ public:
     /// assign the fields in OpenFOAM based on the scalar list of states
     void list2OFField(
         const scalarList& stateList,
-        const scalarList& stateBounaryList) const;
+        const scalarList& stateBounaryList,
+        const label oldTimeLevel) const;
 
     /// set the boundary conditions based on parameters defined in DAOption
     void setPrimalBoundaryConditions(const label printInfo = 1);
diff --git a/src/adjoint/DAFvSource/DAFvSourceActuatorDisk.C b/src/adjoint/DAFvSource/DAFvSourceActuatorDisk.C
index 13f0a94d..7d1fa422 100755
--- a/src/adjoint/DAFvSource/DAFvSourceActuatorDisk.C
+++ b/src/adjoint/DAFvSource/DAFvSourceActuatorDisk.C
@@ -46,6 +46,9 @@ void DAFvSourceActuatorDisk::calcFvSource(volVectorField& fvSource)
         source = rStar * sqrt(1.0 - rStar) * scale
         where rStar is the normalized radial location and scale is used to 
         make sure the integral force equals the desired total thrust
+        
+        NOTE: rotDir = right means propeller rotates clockwise viewed from 
+        the tail of the aircraft looking forward
 
         There are two options to assign the source term:
         1. cylinderAnnulusToCell. Users prescribe a cylinderAnnulus and the fvSource will be
@@ -161,13 +164,13 @@ void DAFvSourceActuatorDisk::calcFvSource(volVectorField& fvSource)
                 vector cellC2AVecC(vector::zero);
                 if (rotDir == "left")
                 {
-                    // this assumes right hand rotation of propellers
-                    cellC2AVecC = cellC2AVecR ^ cellC2AVecA; // circ
+                    // propeller rotates counter-clockwise viewed from the tail of the aircraft looking forward
+                    cellC2AVecC = cellC2AVecR ^ diskDirNorm; // circ
                 }
                 else if (rotDir == "right")
                 {
-                    // this assumes left hand rotation of propellers
-                    cellC2AVecC = cellC2AVecA ^ cellC2AVecR; // circ
+                    // propeller rotates clockwise viewed from the tail of the aircraft looking forward
+                    cellC2AVecC = diskDirNorm ^ cellC2AVecR; // circ
                 }
                 else
                 {
@@ -244,7 +247,7 @@ void DAFvSourceActuatorDisk::calcFvSource(volVectorField& fvSource)
             scalar fRMin = pow(rStarMin, expM) * pow(1.0 - rStarMin, expN);
             scalar fRMax = pow(rStarMax, expM) * pow(1.0 - rStarMax, expN);
 
-            label adjustThrust = diskSubDict.lookupOrDefault<label>("adjustThrust", 0);
+            label adjustThrust = diskSubDict.getLabel("adjustThrust");
             // if adjustThrust = False, we just read "scale" from daOption
             // if we want to adjust thrust, we calculate scale, instead of reading from daOption
             // to calculate the scale, we just compute the fAxial with scale = 1, then we find
@@ -341,13 +344,13 @@ void DAFvSourceActuatorDisk::calcFvSource(volVectorField& fvSource)
                 vector cellC2AVecC(vector::zero);
                 if (rotDir == "left")
                 {
-                    // this assumes right hand rotation of propellers
-                    cellC2AVecC = cellC2AVecR ^ cellC2AVecA; // circ
+                    // propeller rotates counter-clockwise viewed from the tail of the aircraft looking forward
+                    cellC2AVecC = cellC2AVecR ^ dirNorm; // circ
                 }
                 else if (rotDir == "right")
                 {
-                    // this assumes left hand rotation of propellers
-                    cellC2AVecC = cellC2AVecA ^ cellC2AVecR; // circ
+                    // propeller rotates clockwise viewed from the tail of the aircraft looking forward
+                    cellC2AVecC = dirNorm ^ cellC2AVecR; // circ
                 }
                 else
                 {
@@ -370,8 +373,6 @@ void DAFvSourceActuatorDisk::calcFvSource(volVectorField& fvSource)
                 scalar rStar = (rPrime - rPrimeHub) / (1.0 - rPrimeHub);
 
                 scalar fAxial = 0.0;
-                scalar fCirc = 0.0;
-
                 scalar dA2 = cellC2AVecALen * cellC2AVecALen;
 
                 if (rStar < rStarMin)
@@ -379,22 +380,22 @@ void DAFvSourceActuatorDisk::calcFvSource(volVectorField& fvSource)
                     scalar dR2 = (rStar - rStarMin) * (rStar - rStarMin);
                     scalar fR = fRMin * exp(-dR2 / epsRStar / epsRStar) * scale;
                     fAxial = fR * exp(-dA2 / eps / eps);
-                    fCirc = fAxial * POD / constant::mathematical::pi / rStarMin;
                 }
                 else if (rStar >= rStarMin && rStar <= rStarMax)
                 {
                     scalar fR = pow(rStar, expM) * pow(1.0 - rStar, expN) * scale;
                     fAxial = fR * exp(-dA2 / eps / eps);
-                    // we use Hoekstra's method to calculate the fCirc based on fAxial
-                    fCirc = fAxial * POD / constant::mathematical::pi / rPrime;
                 }
                 else
                 {
                     scalar dR2 = (rStar - rStarMax) * (rStar - rStarMax);
                     scalar fR = fRMax * exp(-dR2 / epsRStar / epsRStar) * scale;
                     fAxial = fR * exp(-dA2 / eps / eps);
-                    fCirc = fAxial * POD / constant::mathematical::pi / rStarMax;
                 }
+                // we use Hoekstra's method to calculate the fCirc based on fAxial
+                // here we add 0.01*eps/outerRadius to avoid diving a zero rPrime
+                // this might happen if a cell center is very close to actuator center
+                scalar fCirc = fAxial * POD / constant::mathematical::pi / (rPrime + 0.01 * eps / outerRadius);
 
                 vector sourceVec = (fAxial * dirNorm + fCirc * cellC2AVecCNorm);
                 // the source is the force normalized by the cell volume
diff --git a/src/adjoint/DAFvSource/DAFvSourceActuatorLine.C b/src/adjoint/DAFvSource/DAFvSourceActuatorLine.C
index 4e32486b..3bd51bed 100755
--- a/src/adjoint/DAFvSource/DAFvSourceActuatorLine.C
+++ b/src/adjoint/DAFvSource/DAFvSourceActuatorLine.C
@@ -35,6 +35,8 @@ void DAFvSourceActuatorLine::calcFvSource(volVectorField& fvSource)
         Compute the actuator line source term. 
         Reference:  Stokkermans et al. Validation and comparison of RANS propeller 
         modeling methods for tip-mounted applications
+        NOTE: rotDir = right means propeller rotates clockwise viewed from 
+        the tail of the aircraft looking forward
     */
 
     const scalar& pi = Foam::constant::mathematical::pi;
@@ -96,8 +98,8 @@ void DAFvSourceActuatorLine::calcFvSource(volVectorField& fvSource)
         scalar expM = lineSubDict.getScalar("expM");
         scalar expN = lineSubDict.getScalar("expN");
         // Now we need to compute normalized eps in the radial direction, i.e. epsRStar this is because
-        // we need to smooth the radial distribution of the thrust, here the radial location is 
-        // normalized as rStar = (r - rInner) / (rOuter - rInner), so to make epsRStar consistent with this 
+        // we need to smooth the radial distribution of the thrust, here the radial location is
+        // normalized as rStar = (r - rInner) / (rOuter - rInner), so to make epsRStar consistent with this
         // we need to normalize eps with the demoninator of rStar, i.e. Outer - rInner
         scalar epsRStar = eps / (outerRadius - innerRadius);
         scalar rStarMin = epsRStar;
@@ -128,13 +130,13 @@ void DAFvSourceActuatorLine::calcFvSource(volVectorField& fvSource)
             vector cellC2AVecC(vector::zero);
             if (rotDir == "left")
             {
-                // this assumes right hand rotation of propellers
-                cellC2AVecC = cellC2AVecR ^ cellC2AVecA; // circ
+                // propeller rotates counter-clockwise viewed from the tail of the aircraft looking forward
+                cellC2AVecC = cellC2AVecR ^ direction; // circ
             }
             else if (rotDir == "right")
             {
-                // this assumes left hand rotation of propellers
-                cellC2AVecC = cellC2AVecA ^ cellC2AVecR; // circ
+                // propeller rotates clockwise viewed from the tail of the aircraft looking forward
+                cellC2AVecC = direction ^ cellC2AVecR; // circ
             }
             else
             {
@@ -205,27 +207,26 @@ void DAFvSourceActuatorLine::calcFvSource(volVectorField& fvSource)
             scalar rStar = (rPrime - rPrimeHub) / (1.0 - rPrimeHub);
 
             scalar fAxial = 0.0;
-            scalar fCirc = 0.0;
             scalar rPrimeMin = rStarMin * (1.0 - rPrimeHub) + rPrimeHub;
             scalar rPrimeMax = rStarMax * (1.0 - rPrimeHub) + rPrimeHub;
             if (rStar < rStarMin)
             {
                 scalar dR2 = (rStar - rStarMin) * (rStar - rStarMin);
                 fAxial = fRMin * exp(-dR2 / epsRStar / epsRStar);
-                fCirc = fAxial * POD / pi / rPrimeMin;
             }
             else if (rStar >= rStarMin && rStar <= rStarMax)
             {
                 fAxial = pow(rStar, expM) * pow(1.0 - rStar, expN);
-                // we use Hoekstra's method to calculate the fCirc based on fAxial
-                fCirc = fAxial * POD / pi / rPrime;
             }
             else
             {
                 scalar dR2 = (rStar - rStarMax) * (rStar - rStarMax);
                 fAxial = fRMax * exp(-dR2 / epsRStar / epsRStar);
-                fCirc = fAxial * POD / pi / rPrimeMax;
             }
+            // we use Hoekstra's method to calculate the fCirc based on fAxial
+            // here we add 0.01*eps/outerRadius to avoid diving a zero rPrime
+            // this might happen if a cell center is very close to actuator center
+            scalar fCirc = fAxial * POD / pi / (rPrime + 0.01 * eps / outerRadius);
 
             vector sourceVec = (fAxial * direction + fCirc * cellC2AVecCNorm);
 
diff --git a/src/adjoint/DAIndex/DAIndex.C b/src/adjoint/DAIndex/DAIndex.C
index ed4aa40c..9eff5485 100755
--- a/src/adjoint/DAIndex/DAIndex.C
+++ b/src/adjoint/DAIndex/DAIndex.C
@@ -349,9 +349,13 @@ void DAIndex::calcStateLocalIndexOffset(HashTable<label>& offset)
         forAll(phiAccumulatdOffset, idxI)
         {
             if (idxI == 0)
+            {
                 phiAccumulatdOffset[idxI] = 0;
+            }
             else
+            {
                 phiAccumulatdOffset[idxI] = cellOwnedFaces[idxI - 1].size() + phiAccumulatdOffset[idxI - 1];
+            }
         }
         //Info<<"phiAccumulatdOffset "<<phiAccumulatdOffset<<endl;
 
diff --git a/src/adjoint/DAIntmdVar/DAIntmdVar.C b/src/adjoint/DAIntmdVar/DAIntmdVar.C
index 770aebfe..f5b7810d 100755
--- a/src/adjoint/DAIntmdVar/DAIntmdVar.C
+++ b/src/adjoint/DAIntmdVar/DAIntmdVar.C
@@ -114,11 +114,16 @@ void DAIntmdVar::update()
                     volScalarField& intmdField = volScalarList_[idxI];
                     if (nIdx != 0)
                     {
-                        // no need to compute Mean for nIdx = 0 because it will be assigned baseState 
-                        // when restart begines, i.e., nIdx = 1
+                        // if nIdx != 0, we use nIdx to compute beta
                         scalar beta = 1.0 / nIdx;
                         intmdField = beta * baseState + (1.0 - beta) * intmdField;
                     }
+                    else
+                    {
+                        // if nIdx == 0, we use restartSteps to compute beta
+                        scalar beta = 1.0 / restartSteps;
+                        intmdField = beta * baseState + (1.0 - beta) * intmdField;
+                    }
                 }
                 else if (fieldType == "volVectorField")
                 {
@@ -126,11 +131,16 @@ void DAIntmdVar::update()
                     volVectorField& intmdField = volVectorList_[idxI];
                     if (nIdx != 0)
                     {
-                        // no need to compute Mean for nIdx = 0 because it will be assigned baseState  
-                        // when restart begines, i.e., nIdx = 1
+                        // if nIdx != 0, we use nIdx to compute beta
                         scalar beta = 1.0 / nIdx;
                         intmdField = beta * baseState + (1.0 - beta) * intmdField;
                     }
+                    else
+                    {
+                        // if nIdx == 0, we use restartSteps to compute beta
+                        scalar beta = 1.0 / restartSteps;
+                        intmdField = beta * baseState + (1.0 - beta) * intmdField;
+                    }
                 }
             }
         }
diff --git a/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmaras.C b/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmaras.C
index 1bfc4282..a66e41cd 100755
--- a/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmaras.C
+++ b/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmaras.C
@@ -74,14 +74,6 @@ DASpalartAllmaras::DASpalartAllmaras(
           dimensionedScalar("nuTildaRes", dimensionSet(0, 2, -2, 0, 0, 0, 0), 0.0),
 #endif
           zeroGradientFvPatchField<scalar>::typeName),
-      nuTildaResPartDeriv_(
-          IOobject(
-              "nuTildaResPartDeriv",
-              mesh.time().timeName(),
-              mesh,
-              IOobject::NO_READ,
-              IOobject::NO_WRITE),
-          nuTildaRes_),
       y_(mesh.thisDb().lookupObject<volScalarField>("yWall"))
 {
 
diff --git a/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmaras.H b/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmaras.H
index cf4d97ed..0a161e5f 100755
--- a/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmaras.H
+++ b/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmaras.H
@@ -63,7 +63,6 @@ protected:
     //@{
     volScalarField& nuTilda_;
     volScalarField nuTildaRes_;
-    volScalarField nuTildaResPartDeriv_;
     //@}
 
     /// 3D wall distance
diff --git a/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmarasFv3.C b/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmarasFv3.C
index b3503c3b..c9455ed8 100755
--- a/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmarasFv3.C
+++ b/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmarasFv3.C
@@ -74,14 +74,6 @@ DASpalartAllmarasFv3::DASpalartAllmarasFv3(
           dimensionedScalar("nuTildaRes", dimensionSet(0, 2, -2, 0, 0, 0, 0), 0.0),
 #endif
           zeroGradientFvPatchField<scalar>::typeName),
-      nuTildaResPartDeriv_(
-          IOobject(
-              "nuTildaResPartDeriv",
-              mesh.time().timeName(),
-              mesh,
-              IOobject::NO_READ,
-              IOobject::NO_WRITE),
-          nuTildaRes_),
       y_(mesh.thisDb().lookupObject<volScalarField>("yWall"))
 {
 
diff --git a/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmarasFv3.H b/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmarasFv3.H
index 57a1bcd8..04cf98a7 100755
--- a/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmarasFv3.H
+++ b/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmarasFv3.H
@@ -63,7 +63,6 @@ protected:
     //@{
     volScalarField& nuTilda_;
     volScalarField nuTildaRes_;
-    volScalarField nuTildaResPartDeriv_;
     //@}
 
     /// 3D wall distance
diff --git a/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmarasFv3Beta.C b/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmarasFv3Beta.C
index 933850eb..2961c50e 100755
--- a/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmarasFv3Beta.C
+++ b/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmarasFv3Beta.C
@@ -74,14 +74,6 @@ DASpalartAllmarasFv3Beta::DASpalartAllmarasFv3Beta(
           dimensionedScalar("nuTildaRes", dimensionSet(0, 2, -2, 0, 0, 0, 0), 0.0),
 #endif
           zeroGradientFvPatchField<scalar>::typeName),
-      nuTildaResPartDeriv_(
-          IOobject(
-              "nuTildaResPartDeriv",
-              mesh.time().timeName(),
-              mesh,
-              IOobject::NO_READ,
-              IOobject::NO_WRITE),
-          nuTildaRes_),
       betaSA_(const_cast<volScalarField&>(
           mesh.thisDb().lookupObject<volScalarField>("betaSA"))),
       betaSATrue_(const_cast<volScalarField&>(
diff --git a/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmarasFv3Beta.H b/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmarasFv3Beta.H
index ded09c30..62ef63ae 100755
--- a/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmarasFv3Beta.H
+++ b/src/adjoint/DAModel/DATurbulenceModel/DASpalartAllmarasFv3Beta.H
@@ -65,7 +65,6 @@ protected:
     //@{
     volScalarField& nuTilda_;
     volScalarField nuTildaRes_;
-    volScalarField nuTildaResPartDeriv_;
     //@}
 
     /// A beta field multiplying to the production term
diff --git a/src/adjoint/DAModel/DATurbulenceModel/DAkOmega.C b/src/adjoint/DAModel/DATurbulenceModel/DAkOmega.C
index 89e7e20c..dda25d24 100755
--- a/src/adjoint/DAModel/DATurbulenceModel/DAkOmega.C
+++ b/src/adjoint/DAModel/DATurbulenceModel/DAkOmega.C
@@ -60,14 +60,6 @@ DAkOmega::DAkOmega(
           dimensionedScalar("omegaRes", dimensionSet(0, 0, -2, 0, 0, 0, 0), 0.0),
 #endif
           zeroGradientFvPatchField<scalar>::typeName),
-      omegaResPartDeriv_(
-          IOobject(
-              "omegaResPartDeriv",
-              mesh.time().timeName(),
-              mesh,
-              IOobject::NO_READ,
-              IOobject::NO_WRITE),
-          omegaRes_),
       k_(
           const_cast<volScalarField&>(
               mesh_.thisDb().lookupObject<volScalarField>("k"))),
@@ -85,15 +77,7 @@ DAkOmega::DAkOmega(
 #ifdef IncompressibleFlow
           dimensionedScalar("kRes", dimensionSet(0, 2, -3, 0, 0, 0, 0), 0.0),
 #endif
-          zeroGradientFvPatchField<scalar>::typeName),
-      kResPartDeriv_(
-          IOobject(
-              "kResPartDeriv",
-              mesh.time().timeName(),
-              mesh,
-              IOobject::NO_READ,
-              IOobject::NO_WRITE),
-          kRes_)
+          zeroGradientFvPatchField<scalar>::typeName)
 {
 
     // initialize printInterval_ we need to check whether it is a steady state
diff --git a/src/adjoint/DAModel/DATurbulenceModel/DAkOmega.H b/src/adjoint/DAModel/DATurbulenceModel/DAkOmega.H
index 5ab9baf1..57db127f 100755
--- a/src/adjoint/DAModel/DATurbulenceModel/DAkOmega.H
+++ b/src/adjoint/DAModel/DATurbulenceModel/DAkOmega.H
@@ -70,10 +70,8 @@ protected:
     //@{
     volScalarField& omega_;
     volScalarField omegaRes_;
-    volScalarField omegaResPartDeriv_;
     volScalarField& k_;
     volScalarField kRes_;
-    volScalarField kResPartDeriv_;
     //@}
 
     /// cell-center omega values near the wall, this is to fix the issue that the
diff --git a/src/adjoint/DAModel/DATurbulenceModel/DAkOmegaSST.C b/src/adjoint/DAModel/DATurbulenceModel/DAkOmegaSST.C
index f59e9080..61fc9808 100755
--- a/src/adjoint/DAModel/DATurbulenceModel/DAkOmegaSST.C
+++ b/src/adjoint/DAModel/DATurbulenceModel/DAkOmegaSST.C
@@ -92,14 +92,6 @@ DAkOmegaSST::DAkOmegaSST(
           dimensionedScalar("omegaRes", dimensionSet(0, 0, -2, 0, 0, 0, 0), 0.0),
 #endif
           zeroGradientFvPatchField<scalar>::typeName),
-      omegaResPartDeriv_(
-          IOobject(
-              "omegaResPartDeriv",
-              mesh.time().timeName(),
-              mesh,
-              IOobject::NO_READ,
-              IOobject::NO_WRITE),
-          omegaRes_),
       k_(
           const_cast<volScalarField&>(
               mesh_.thisDb().lookupObject<volScalarField>("k"))),
@@ -118,14 +110,6 @@ DAkOmegaSST::DAkOmegaSST(
           dimensionedScalar("kRes", dimensionSet(0, 2, -3, 0, 0, 0, 0), 0.0),
 #endif
           zeroGradientFvPatchField<scalar>::typeName),
-      kResPartDeriv_(
-          IOobject(
-              "kResPartDeriv",
-              mesh.time().timeName(),
-              mesh,
-              IOobject::NO_READ,
-              IOobject::NO_WRITE),
-          kRes_),
       y_(mesh_.thisDb().lookupObject<volScalarField>("yWall"))
 {
 
diff --git a/src/adjoint/DAModel/DATurbulenceModel/DAkOmegaSST.H b/src/adjoint/DAModel/DATurbulenceModel/DAkOmegaSST.H
index b1587fef..7517b3fa 100755
--- a/src/adjoint/DAModel/DATurbulenceModel/DAkOmegaSST.H
+++ b/src/adjoint/DAModel/DATurbulenceModel/DAkOmegaSST.H
@@ -141,10 +141,8 @@ protected:
     //@{
     volScalarField& omega_;
     volScalarField omegaRes_;
-    volScalarField omegaResPartDeriv_;
     volScalarField& k_;
     volScalarField kRes_;
-    volScalarField kResPartDeriv_;
     //@}
 
     /// 3D wall distance
diff --git a/src/adjoint/DAModel/DATurbulenceModel/DAkOmegaSSTLM.C b/src/adjoint/DAModel/DATurbulenceModel/DAkOmegaSSTLM.C
index c3236f4f..88813615 100755
--- a/src/adjoint/DAModel/DATurbulenceModel/DAkOmegaSSTLM.C
+++ b/src/adjoint/DAModel/DATurbulenceModel/DAkOmegaSSTLM.C
@@ -119,14 +119,6 @@ DAkOmegaSSTLM::DAkOmegaSSTLM(
           dimensionedScalar("omegaRes", dimensionSet(0, 0, -2, 0, 0, 0, 0), 0.0),
 #endif
           zeroGradientFvPatchField<scalar>::typeName),
-      omegaResPartDeriv_(
-          IOobject(
-              "omegaResPartDeriv",
-              mesh.time().timeName(),
-              mesh,
-              IOobject::NO_READ,
-              IOobject::NO_WRITE),
-          omegaRes_),
       k_(const_cast<volScalarField&>(
           mesh_.thisDb().lookupObject<volScalarField>("k"))),
       kRes_(
@@ -144,14 +136,6 @@ DAkOmegaSSTLM::DAkOmegaSSTLM(
           dimensionedScalar("kRes", dimensionSet(0, 2, -3, 0, 0, 0, 0), 0.0),
 #endif
           zeroGradientFvPatchField<scalar>::typeName),
-      kResPartDeriv_(
-          IOobject(
-              "kResPartDeriv",
-              mesh.time().timeName(),
-              mesh,
-              IOobject::NO_READ,
-              IOobject::NO_WRITE),
-          kRes_),
       ReThetat_(const_cast<volScalarField&>(
           mesh_.thisDb().lookupObject<volScalarField>("ReThetat"))),
       ReThetatRes_(
@@ -169,14 +153,6 @@ DAkOmegaSSTLM::DAkOmegaSSTLM(
           dimensionedScalar("ReThetatRes", dimensionSet(0, 0, -1, 0, 0, 0, 0), 0.0),
 #endif
           zeroGradientFvPatchScalarField::typeName),
-      ReThetatResPartDeriv_(
-          IOobject(
-              "ReThetatResPartDeriv",
-              mesh_.time().timeName(),
-              mesh_,
-              IOobject::NO_READ,
-              IOobject::NO_WRITE),
-          ReThetatRes_),
       gammaInt_(const_cast<volScalarField&>(
           mesh_.thisDb().lookupObject<volScalarField>("gammaInt"))),
       gammaIntRes_(
@@ -194,14 +170,6 @@ DAkOmegaSSTLM::DAkOmegaSSTLM(
           dimensionedScalar("gammaIntRes", dimensionSet(0, 0, -1, 0, 0, 0, 0), 0.0),
 #endif
           zeroGradientFvPatchScalarField::typeName),
-      gammaIntResPartDeriv_(
-          IOobject(
-              "gammaIntResPartDeriv",
-              mesh_.time().timeName(),
-              mesh_,
-              IOobject::NO_READ,
-              IOobject::NO_WRITE),
-          gammaIntRes_),
       gammaIntEff_(const_cast<volScalarField::Internal&>(
           mesh_.thisDb().lookupObject<volScalarField::Internal>("gammaIntEff"))),
       y_(mesh_.thisDb().lookupObject<volScalarField>("yWall"))
diff --git a/src/adjoint/DAModel/DATurbulenceModel/DAkOmegaSSTLM.H b/src/adjoint/DAModel/DATurbulenceModel/DAkOmegaSSTLM.H
index a6d2de32..190819e3 100755
--- a/src/adjoint/DAModel/DATurbulenceModel/DAkOmegaSSTLM.H
+++ b/src/adjoint/DAModel/DATurbulenceModel/DAkOmegaSSTLM.H
@@ -178,16 +178,12 @@ protected:
     //@{
     volScalarField& omega_;
     volScalarField omegaRes_;
-    volScalarField omegaResPartDeriv_;
     volScalarField& k_;
     volScalarField kRes_;
-    volScalarField kResPartDeriv_;
     volScalarField& ReThetat_; // Transition onset momentum-thickness Reynolds number
     volScalarField ReThetatRes_;
-    volScalarField ReThetatResPartDeriv_;
     volScalarField& gammaInt_; // Intermittency
     volScalarField gammaIntRes_;
-    volScalarField gammaIntResPartDeriv_;
     //@}
 
     /// Effective intermittency
diff --git a/src/adjoint/DAResidual/DAResidualLaplacianFoam.C b/src/adjoint/DAResidual/DAResidualLaplacianFoam.C
new file mode 100755
index 00000000..1d6fada1
--- /dev/null
+++ b/src/adjoint/DAResidual/DAResidualLaplacianFoam.C
@@ -0,0 +1,102 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+\*---------------------------------------------------------------------------*/
+
+#include "DAResidualLaplacianFoam.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+defineTypeNameAndDebug(DAResidualLaplacianFoam, 0);
+addToRunTimeSelectionTable(DAResidual, DAResidualLaplacianFoam, dictionary);
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+DAResidualLaplacianFoam::DAResidualLaplacianFoam(
+    const word modelType,
+    const fvMesh& mesh,
+    const DAOption& daOption,
+    const DAModel& daModel,
+    const DAIndex& daIndex)
+    : DAResidual(modelType, mesh, daOption, daModel, daIndex),
+      // initialize and register state variables and their residuals, we use macros defined in macroFunctions.H
+      setResidualClassMemberScalar(T, dimensionSet(0, 0, -1, 1, 0, 0, 0))
+
+{
+    IOdictionary transportProperties(
+        IOobject(
+            "transportProperties",
+            mesh_.time().constant(),
+            mesh_,
+            IOobject::MUST_READ,
+            IOobject::NO_WRITE));
+
+    dimensionedScalar DT("DT", dimViscosity, transportProperties);
+
+    DT_ = DT.value();
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+void DAResidualLaplacianFoam::clear()
+{
+    /*
+    Description:
+        Clear all members to avoid memory leak because we will initalize 
+        multiple objects of DAResidual. Here we need to delete all members
+        in the parent and child classes
+    */
+    TRes_.clear();
+}
+
+void DAResidualLaplacianFoam::calcResiduals(const dictionary& options)
+{
+    /*
+    Description:
+        This is the function to compute residuals.
+    
+    Input:
+        options.isPC: 1 means computing residuals for preconditioner matrix.
+        This essentially use the first order scheme for div(phi,U), div(phi,e)
+
+        p_, T_, U_, phi_, etc: State variables in OpenFOAM
+    
+    Output:
+        URes_, pRes_, TRes_, phiRes_: residual field variables
+    */
+
+    dimensionedScalar DT("DT", dimViscosity, DT_);
+
+    fvScalarMatrix TEqn(
+        fvm::ddt(T_)
+        - fvm::laplacian(DT, T_));
+
+    TRes_ = TEqn & T_;
+    normalizeResiduals(TRes);
+}
+
+void DAResidualLaplacianFoam::updateIntermediateVariables()
+{
+    /* 
+    Description:
+        Update the intermediate variables that depend on the state variables
+    */
+    // do nothing
+}
+
+void DAResidualLaplacianFoam::correctBoundaryConditions()
+{
+    /* 
+    Description:
+        Update the boundary condition for all the states in the selected solver
+    */
+
+    T_.correctBoundaryConditions();
+}
+
+} // End namespace Foam
+
+// ************************************************************************* //
diff --git a/src/adjoint/DAResidual/DAResidualLaplacianFoam.H b/src/adjoint/DAResidual/DAResidualLaplacianFoam.H
new file mode 100755
index 00000000..558b2acc
--- /dev/null
+++ b/src/adjoint/DAResidual/DAResidualLaplacianFoam.H
@@ -0,0 +1,79 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+    Description:
+        Child class for DALaplacianFoam
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef DAResidualLaplacianFoam_H
+#define DAResidualLaplacianFoam_H
+
+#include "DAResidual.H"
+#include "addToRunTimeSelectionTable.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+/*---------------------------------------------------------------------------*\
+      Class DAResidualLaplacianFoam Declaration
+\*---------------------------------------------------------------------------*/
+
+class DAResidualLaplacianFoam
+    : public DAResidual
+{
+
+protected:
+    /// \name These are state variables, state residuals, and partial derivatives
+    //@{
+    volScalarField& T_;
+    volScalarField TRes_;
+    //@}
+
+    scalar DT_;
+
+public:
+    TypeName("DALaplacianFoam");
+    // Constructors
+
+    //- Construct from components
+    DAResidualLaplacianFoam(
+        const word modelType,
+        const fvMesh& mesh,
+        const DAOption& daOption,
+        const DAModel& daModel,
+        const DAIndex& daIndex);
+
+    //- Destructor
+    virtual ~DAResidualLaplacianFoam()
+    {
+    }
+
+    // Members
+
+    /// clear the members
+    virtual void clear();
+
+    /// compute residual
+    virtual void calcResiduals(const dictionary& options);
+
+    /// update any intermediate variables that are dependent on state variables and are used in calcResiduals
+    virtual void updateIntermediateVariables();
+
+    /// update the boundary condition for all the states in the selected solver
+    virtual void correctBoundaryConditions();
+};
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //
diff --git a/src/adjoint/DAResidual/DAResidualPimpleFoam.C b/src/adjoint/DAResidual/DAResidualPimpleFoam.C
new file mode 100755
index 00000000..f405679d
--- /dev/null
+++ b/src/adjoint/DAResidual/DAResidualPimpleFoam.C
@@ -0,0 +1,194 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+\*---------------------------------------------------------------------------*/
+
+#include "DAResidualPimpleFoam.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+defineTypeNameAndDebug(DAResidualPimpleFoam, 0);
+addToRunTimeSelectionTable(DAResidual, DAResidualPimpleFoam, dictionary);
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+DAResidualPimpleFoam::DAResidualPimpleFoam(
+    const word modelType,
+    const fvMesh& mesh,
+    const DAOption& daOption,
+    const DAModel& daModel,
+    const DAIndex& daIndex)
+    : DAResidual(modelType, mesh, daOption, daModel, daIndex),
+      // initialize and register state variables and their residuals, we use macros defined in macroFunctions.H
+      setResidualClassMemberVector(U, dimensionSet(0, 1, -2, 0, 0, 0, 0)),
+      setResidualClassMemberScalar(p, dimensionSet(0, 0, -1, 0, 0, 0, 0)),
+      setResidualClassMemberPhi(phi),
+      fvSource_(const_cast<volVectorField&>(
+          mesh_.thisDb().lookupObject<volVectorField>("fvSource"))),
+      daTurb_(const_cast<DATurbulenceModel&>(daModel.getDATurbulenceModel())),
+      // create simpleControl
+      pimple_(const_cast<fvMesh&>(mesh))
+{
+    // initialize fvSource
+    const dictionary& allOptions = daOption.getAllOptions();
+    if (allOptions.subDict("fvSource").toc().size() != 0)
+    {
+        hasFvSource_ = 1;
+    }
+
+    mode_ = daOption.getSubDictOption<word>("unsteadyAdjoint", "mode");
+}
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+void DAResidualPimpleFoam::clear()
+{
+    /*
+    Description:
+        Clear all members to avoid memory leak because we will initalize 
+        multiple objects of DAResidual. Here we need to delete all members
+        in the parent and child classes
+    */
+    URes_.clear();
+    pRes_.clear();
+    phiRes_.clear();
+}
+
+void DAResidualPimpleFoam::calcResiduals(const dictionary& options)
+{
+    /*
+    Description:
+        This is the function to compute residuals.
+    
+    Input:
+        options.isPC: 1 means computing residuals for preconditioner matrix.
+        This essentially use the first order scheme for div(phi,U)
+
+        p_, U_, phi_, etc: State variables in OpenFOAM
+    
+    Output:
+        URes_, pRes_, phiRes_: residual field variables
+    */
+
+    // We dont support MRF and fvOptions so all the related lines are commented
+    // out for now
+
+    // ******** U Residuals **********
+    // copied and modified from UEqn.H
+
+    word divUScheme = "div(phi,U)";
+
+    label isPC = options.getLabel("isPC");
+
+    if (isPC)
+    {
+        divUScheme = "div(pc)";
+    }
+
+    if (hasFvSource_)
+    {
+        DAFvSource& daFvSource(const_cast<DAFvSource&>(
+            mesh_.thisDb().lookupObject<DAFvSource>("DAFvSource")));
+        // update the actuator source term
+        daFvSource.calcFvSource(fvSource_);
+    }
+
+    fvVectorMatrix UEqn(
+        fvm::ddt(U_)
+        + fvm::div(phi_, U_, divUScheme)
+        + daTurb_.divDevReff(U_)
+        - fvSource_);
+
+    if (mode_ == "hybridAdjoint")
+    {
+        UEqn -= fvm::ddt(U_);
+    }
+
+    UEqn.relax();
+
+    URes_ = (UEqn & U_) + fvc::grad(p_);
+    normalizeResiduals(URes);
+
+    // ******** p Residuals **********
+    // copied and modified from pEqn.H
+    // NOTE manually set pRefCell and pRefValue
+    label pRefCell = 0;
+    scalar pRefValue = 0.0;
+
+    volScalarField rAU(1.0 / UEqn.A());
+    //volVectorField HbyA(constrainHbyA(rAU*UEqn.H(), U_, p_));
+    //***************** NOTE *******************
+    // constrainHbyA has been used since OpenFOAM-v1606; however, We do NOT use the constrainHbyA
+    // function in DAFoam because we found it significantly degrades the accuracy of shape derivatives.
+    // Basically, we should not constrain any variable because it will create discontinuity.
+    // Instead, we use the old implementation used in OpenFOAM-3.0+ and before
+    volVectorField HbyA("HbyA", U_);
+    HbyA = rAU * UEqn.H();
+
+    surfaceScalarField phiHbyA(
+        "phiHbyA",
+        fvc::flux(HbyA)
+            + fvc::interpolate(rAU) * fvc::ddtCorr(U_, phi_));
+
+    if (mode_ == "hybridAdjoint")
+    {
+        phiHbyA -= fvc::interpolate(rAU) * fvc::ddtCorr(U_, phi_);
+    }
+
+    adjustPhi(phiHbyA, U_, p_);
+
+    tmp<volScalarField> rAtU(rAU);
+
+    if (pimple_.consistent())
+    {
+        rAtU = 1.0 / max(1.0 / rAU - UEqn.H1(), 0.1 / rAU);
+        phiHbyA +=
+            fvc::interpolate(rAtU() - rAU) * fvc::snGrad(p_) * mesh_.magSf();
+        HbyA -= (rAU - rAtU()) * fvc::grad(p_);
+    }
+
+    fvScalarMatrix pEqn(
+        fvm::laplacian(rAtU(), p_)
+        == fvc::div(phiHbyA));
+
+    pEqn.setReference(pRefCell, pRefValue);
+
+    pRes_ = pEqn & p_;
+    normalizeResiduals(pRes);
+
+    // ******** phi Residuals **********
+    // copied and modified from pEqn.H
+    phiRes_ = phiHbyA - pEqn.flux() - phi_;
+    // need to normalize phiRes
+    normalizePhiResiduals(phiRes);
+}
+
+void DAResidualPimpleFoam::updateIntermediateVariables()
+{
+    /* 
+    Description:
+        Update the intermediate variables that depend on the state variables
+    */
+
+    // nothing to update for DAPimpleFoam
+}
+
+void DAResidualPimpleFoam::correctBoundaryConditions()
+{
+    /* 
+    Description:
+        Update the boundary condition for all the states in the selected solver
+    */
+
+    U_.correctBoundaryConditions();
+    p_.correctBoundaryConditions();
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// ************************************************************************* //
diff --git a/src/adjoint/DAResidual/DAResidualPimpleFoam.H b/src/adjoint/DAResidual/DAResidualPimpleFoam.H
new file mode 100755
index 00000000..b9f5ec3c
--- /dev/null
+++ b/src/adjoint/DAResidual/DAResidualPimpleFoam.H
@@ -0,0 +1,99 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+    Description:
+        Child class for DAPimpleFoam
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef DAResidualPimpleFoam_H
+#define DAResidualPimpleFoam_H
+
+#include "DAResidual.H"
+#include "addToRunTimeSelectionTable.H"
+#include "pimpleControl.H"
+#include "adjustPhi.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+/*---------------------------------------------------------------------------*\
+      Class DAResidualPimpleFoam Declaration
+\*---------------------------------------------------------------------------*/
+
+class DAResidualPimpleFoam
+    : public DAResidual
+{
+protected:
+    /// \name These are state variables, state residuals, and partial derivatives
+    //@{
+    volVectorField& U_;
+    volVectorField URes_;
+
+    volScalarField& p_;
+    volScalarField pRes_;
+
+    surfaceScalarField& phi_;
+    surfaceScalarField phiRes_;
+    //@}
+
+    /// fvSource term
+    volVectorField& fvSource_;
+
+    /// DATurbulenceModel object
+    DATurbulenceModel& daTurb_;
+
+    /// pimpleControl object which will be initialized in this class
+    pimpleControl pimple_;
+
+    /// whether to has fvSource term
+    label hasFvSource_ = 0;
+
+    /// whether the hybrid adjoint or time accurate adjoint is active
+    word mode_ = "None";
+
+public:
+    TypeName("DAPimpleFoam");
+    // Constructors
+
+    //- Construct from components
+    DAResidualPimpleFoam(
+        const word modelType,
+        const fvMesh& mesh,
+        const DAOption& daOption,
+        const DAModel& daModel,
+        const DAIndex& daIndex);
+
+    //- Destructor
+    virtual ~DAResidualPimpleFoam()
+    {
+    }
+
+    // Members
+
+    /// clear the members
+    virtual void clear();
+    
+    /// compute residual
+    virtual void calcResiduals(const dictionary& options);
+
+    /// update any intermediate variables that are dependent on state variables and are used in calcResiduals
+    virtual void updateIntermediateVariables();
+
+    /// update the boundary condition for all the states in the selected solver
+    virtual void correctBoundaryConditions();
+};
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //
diff --git a/src/adjoint/DAResidual/DAResidualPisoFoam.C b/src/adjoint/DAResidual/DAResidualPisoFoam.C
index ac999549..800765d2 100755
--- a/src/adjoint/DAResidual/DAResidualPisoFoam.C
+++ b/src/adjoint/DAResidual/DAResidualPisoFoam.C
@@ -39,6 +39,9 @@ DAResidualPisoFoam::DAResidualPisoFoam(
     {
         hasFvSource_ = 1;
     }
+
+    mode_ = daOption.getSubDictOption<word>("unsteadyAdjoint", "mode");
+
 }
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
@@ -52,11 +55,8 @@ void DAResidualPisoFoam::clear()
         in the parent and child classes
     */
     URes_.clear();
-    UResPartDeriv_.clear();
     pRes_.clear();
-    pResPartDeriv_.clear();
     phiRes_.clear();
-    phiResPartDeriv_.clear();
 }
 
 void DAResidualPisoFoam::calcResiduals(const dictionary& options)
@@ -93,16 +93,22 @@ void DAResidualPisoFoam::calcResiduals(const dictionary& options)
     if (hasFvSource_)
     {
         DAFvSource& daFvSource(const_cast<DAFvSource&>(
-          mesh_.thisDb().lookupObject<DAFvSource>("DAFvSource")));
+            mesh_.thisDb().lookupObject<DAFvSource>("DAFvSource")));
         // update the actuator source term
         daFvSource.calcFvSource(fvSource_);
     }
 
     fvVectorMatrix UEqn(
-        fvm::div(phi_, U_, divUScheme)
+        fvm::ddt(U_)
+        + fvm::div(phi_, U_, divUScheme)
         + daTurb_.divDevReff(U_)
         - fvSource_);
 
+    if (mode_ == "hybridAdjoint")
+    {
+        UEqn -= fvm::ddt(U_);
+    }
+
     UEqn.relax();
 
     URes_ = (UEqn & U_) + fvc::grad(p_);
@@ -124,7 +130,15 @@ void DAResidualPisoFoam::calcResiduals(const dictionary& options)
     volVectorField HbyA("HbyA", U_);
     HbyA = rAU * UEqn.H();
 
-    surfaceScalarField phiHbyA("phiHbyA", fvc::flux(HbyA));
+    surfaceScalarField phiHbyA(
+        "phiHbyA",
+        fvc::flux(HbyA)
+            + fvc::interpolate(rAU) * fvc::ddtCorr(U_, phi_));
+
+    if (mode_ == "hybridAdjoint")
+    {
+        phiHbyA -= fvc::interpolate(rAU) * fvc::ddtCorr(U_, phi_);
+    }
 
     adjustPhi(phiHbyA, U_, p_);
 
diff --git a/src/adjoint/DAResidual/DAResidualPisoFoam.H b/src/adjoint/DAResidual/DAResidualPisoFoam.H
index 2837c537..bd0f5bbf 100755
--- a/src/adjoint/DAResidual/DAResidualPisoFoam.H
+++ b/src/adjoint/DAResidual/DAResidualPisoFoam.H
@@ -33,15 +33,12 @@ protected:
     //@{
     volVectorField& U_;
     volVectorField URes_;
-    volVectorField UResPartDeriv_;
 
     volScalarField& p_;
     volScalarField pRes_;
-    volScalarField pResPartDeriv_;
 
     surfaceScalarField& phi_;
     surfaceScalarField phiRes_;
-    surfaceScalarField phiResPartDeriv_;
     //@}
 
     /// fvSource term
@@ -56,6 +53,9 @@ protected:
     /// whether to has fvSource term
     label hasFvSource_ = 0;
 
+    /// whether the hybrid adjoint or time accurate adjoint is active
+    word mode_ = "None";
+
 public:
     TypeName("DAPisoFoam");
     // Constructors
diff --git a/src/adjoint/DAResidual/DAResidualRhoSimpleCFoam.C b/src/adjoint/DAResidual/DAResidualRhoSimpleCFoam.C
index deb741ca..f589df85 100755
--- a/src/adjoint/DAResidual/DAResidualRhoSimpleCFoam.C
+++ b/src/adjoint/DAResidual/DAResidualRhoSimpleCFoam.C
@@ -67,13 +67,9 @@ void DAResidualRhoSimpleCFoam::clear()
         in the parent and child classes
     */
     URes_.clear();
-    UResPartDeriv_.clear();
     pRes_.clear();
-    pResPartDeriv_.clear();
     TRes_.clear();
-    TResPartDeriv_.clear();
     phiRes_.clear();
-    phiResPartDeriv_.clear();
 }
 
 void DAResidualRhoSimpleCFoam::calcResiduals(const dictionary& options)
diff --git a/src/adjoint/DAResidual/DAResidualRhoSimpleCFoam.H b/src/adjoint/DAResidual/DAResidualRhoSimpleCFoam.H
index e40c76b6..e9a76627 100755
--- a/src/adjoint/DAResidual/DAResidualRhoSimpleCFoam.H
+++ b/src/adjoint/DAResidual/DAResidualRhoSimpleCFoam.H
@@ -36,19 +36,15 @@ protected:
     //@{
     volVectorField& U_;
     volVectorField URes_;
-    volVectorField UResPartDeriv_;
 
     volScalarField& p_;
     volScalarField pRes_;
-    volScalarField pResPartDeriv_;
 
     volScalarField& T_;
     volScalarField TRes_;
-    volScalarField TResPartDeriv_;
 
     surfaceScalarField& phi_;
     surfaceScalarField phiRes_;
-    surfaceScalarField phiResPartDeriv_;
     //@}
 
     /// thermophysical property
diff --git a/src/adjoint/DAResidual/DAResidualRhoSimpleFoam.C b/src/adjoint/DAResidual/DAResidualRhoSimpleFoam.C
index f2e65bca..539e6143 100755
--- a/src/adjoint/DAResidual/DAResidualRhoSimpleFoam.C
+++ b/src/adjoint/DAResidual/DAResidualRhoSimpleFoam.C
@@ -79,13 +79,9 @@ void DAResidualRhoSimpleFoam::clear()
         in the parent and child classes
     */
     URes_.clear();
-    UResPartDeriv_.clear();
     pRes_.clear();
-    pResPartDeriv_.clear();
     TRes_.clear();
-    TResPartDeriv_.clear();
     phiRes_.clear();
-    phiResPartDeriv_.clear();
 }
 
 void DAResidualRhoSimpleFoam::calcResiduals(const dictionary& options)
diff --git a/src/adjoint/DAResidual/DAResidualRhoSimpleFoam.H b/src/adjoint/DAResidual/DAResidualRhoSimpleFoam.H
index 4d04abe8..7fc31ef3 100755
--- a/src/adjoint/DAResidual/DAResidualRhoSimpleFoam.H
+++ b/src/adjoint/DAResidual/DAResidualRhoSimpleFoam.H
@@ -38,19 +38,15 @@ protected:
     //@{
     volVectorField& U_;
     volVectorField URes_;
-    volVectorField UResPartDeriv_;
 
     volScalarField& p_;
     volScalarField pRes_;
-    volScalarField pResPartDeriv_;
 
     volScalarField& T_;
     volScalarField TRes_;
-    volScalarField TResPartDeriv_;
 
     surfaceScalarField& phi_;
     surfaceScalarField phiRes_;
-    surfaceScalarField phiResPartDeriv_;
     //@}
 
     /// fvSource term
diff --git a/src/adjoint/DAResidual/DAResidualScalarTransportFoam.C b/src/adjoint/DAResidual/DAResidualScalarTransportFoam.C
new file mode 100755
index 00000000..a08fc13f
--- /dev/null
+++ b/src/adjoint/DAResidual/DAResidualScalarTransportFoam.C
@@ -0,0 +1,107 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+\*---------------------------------------------------------------------------*/
+
+#include "DAResidualScalarTransportFoam.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+defineTypeNameAndDebug(DAResidualScalarTransportFoam, 0);
+addToRunTimeSelectionTable(DAResidual, DAResidualScalarTransportFoam, dictionary);
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+DAResidualScalarTransportFoam::DAResidualScalarTransportFoam(
+    const word modelType,
+    const fvMesh& mesh,
+    const DAOption& daOption,
+    const DAModel& daModel,
+    const DAIndex& daIndex)
+    : DAResidual(modelType, mesh, daOption, daModel, daIndex),
+      // initialize and register state variables and their residuals, we use macros defined in macroFunctions.H
+      setResidualClassMemberScalar(T, dimensionSet(0, 0, -1, 1, 0, 0, 0)),
+      phi_(const_cast<surfaceScalarField&>(
+          mesh_.thisDb().lookupObject<surfaceScalarField>("phi")))
+
+{
+    IOdictionary transportProperties(
+        IOobject(
+            "transportProperties",
+            mesh_.time().constant(),
+            mesh_,
+            IOobject::MUST_READ,
+            IOobject::NO_WRITE));
+
+    dimensionedScalar DT("DT", dimViscosity, transportProperties);
+
+    DT_ = DT.value();
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+void DAResidualScalarTransportFoam::clear()
+{
+    /*
+    Description:
+        Clear all members to avoid memory leak because we will initalize 
+        multiple objects of DAResidual. Here we need to delete all members
+        in the parent and child classes
+    */
+    TRes_.clear();
+}
+
+void DAResidualScalarTransportFoam::calcResiduals(const dictionary& options)
+{
+    /*
+    Description:
+        This is the function to compute residuals.
+    
+    Input:
+        options.isPC: 1 means computing residuals for preconditioner matrix.
+        This essentially use the first order scheme for div(phi,U), div(phi,e)
+
+        p_, T_, U_, phi_, etc: State variables in OpenFOAM
+    
+    Output:
+        URes_, pRes_, TRes_, phiRes_: residual field variables
+    */
+
+    dimensionedScalar DT("DT", dimViscosity, DT_);
+
+    fvScalarMatrix TEqn(
+        fvm::ddt(T_)
+        + fvm::div(phi_, T_)
+        - fvm::laplacian(DT, T_));
+
+    TEqn.relax();
+
+    TRes_ = TEqn & T_;
+    normalizeResiduals(TRes);
+}
+
+void DAResidualScalarTransportFoam::updateIntermediateVariables()
+{
+    /* 
+    Description:
+        Update the intermediate variables that depend on the state variables
+    */
+    // do nothing
+}
+
+void DAResidualScalarTransportFoam::correctBoundaryConditions()
+{
+    /* 
+    Description:
+        Update the boundary condition for all the states in the selected solver
+    */
+
+    T_.correctBoundaryConditions();
+}
+
+} // End namespace Foam
+
+// ************************************************************************* //
diff --git a/src/adjoint/DAResidual/DAResidualScalarTransportFoam.H b/src/adjoint/DAResidual/DAResidualScalarTransportFoam.H
new file mode 100755
index 00000000..71a20aaa
--- /dev/null
+++ b/src/adjoint/DAResidual/DAResidualScalarTransportFoam.H
@@ -0,0 +1,80 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+    Description:
+        Child class for DAScalarTransportFoam
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef DAResidualScalarTransportFoam_H
+#define DAResidualScalarTransportFoam_H
+
+#include "DAResidual.H"
+#include "addToRunTimeSelectionTable.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+/*---------------------------------------------------------------------------*\
+      Class DAResidualScalarTransportFoam Declaration
+\*---------------------------------------------------------------------------*/
+
+class DAResidualScalarTransportFoam
+    : public DAResidual
+{
+
+protected:
+    /// \name These are state variables, state residuals, and partial derivatives
+    //@{
+    volScalarField& T_;
+    volScalarField TRes_;
+    surfaceScalarField& phi_;
+    //@}
+
+    scalar DT_;
+
+public:
+    TypeName("DAScalarTransportFoam");
+    // Constructors
+
+    //- Construct from components
+    DAResidualScalarTransportFoam(
+        const word modelType,
+        const fvMesh& mesh,
+        const DAOption& daOption,
+        const DAModel& daModel,
+        const DAIndex& daIndex);
+
+    //- Destructor
+    virtual ~DAResidualScalarTransportFoam()
+    {
+    }
+
+    // Members
+
+    /// clear the members
+    virtual void clear();
+
+    /// compute residual
+    virtual void calcResiduals(const dictionary& options);
+
+    /// update any intermediate variables that are dependent on state variables and are used in calcResiduals
+    virtual void updateIntermediateVariables();
+
+    /// update the boundary condition for all the states in the selected solver
+    virtual void correctBoundaryConditions();
+};
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //
diff --git a/src/adjoint/DAResidual/DAResidualSimpleFoam.C b/src/adjoint/DAResidual/DAResidualSimpleFoam.C
index 335ad8f7..d1fad6d9 100755
--- a/src/adjoint/DAResidual/DAResidualSimpleFoam.C
+++ b/src/adjoint/DAResidual/DAResidualSimpleFoam.C
@@ -55,11 +55,8 @@ void DAResidualSimpleFoam::clear()
         in the parent and child classes
     */
     URes_.clear();
-    UResPartDeriv_.clear();
     pRes_.clear();
-    pResPartDeriv_.clear();
     phiRes_.clear();
-    phiResPartDeriv_.clear();
 }
 
 void DAResidualSimpleFoam::calcResiduals(const dictionary& options)
diff --git a/src/adjoint/DAResidual/DAResidualSimpleFoam.H b/src/adjoint/DAResidual/DAResidualSimpleFoam.H
index 2d94d353..b42ac3ee 100755
--- a/src/adjoint/DAResidual/DAResidualSimpleFoam.H
+++ b/src/adjoint/DAResidual/DAResidualSimpleFoam.H
@@ -35,15 +35,12 @@ protected:
     //@{
     volVectorField& U_;
     volVectorField URes_;
-    volVectorField UResPartDeriv_;
 
     volScalarField& p_;
     volScalarField pRes_;
-    volScalarField pResPartDeriv_;
 
     surfaceScalarField& phi_;
     surfaceScalarField phiRes_;
-    surfaceScalarField phiResPartDeriv_;
     //@}
 
     /// alpha porosity term
diff --git a/src/adjoint/DAResidual/DAResidualSimpleTFoam.C b/src/adjoint/DAResidual/DAResidualSimpleTFoam.C
index 61552ac1..41cfea42 100755
--- a/src/adjoint/DAResidual/DAResidualSimpleTFoam.C
+++ b/src/adjoint/DAResidual/DAResidualSimpleTFoam.C
@@ -60,13 +60,9 @@ void DAResidualSimpleTFoam::clear()
         in the parent and child classes
     */
     URes_.clear();
-    UResPartDeriv_.clear();
     pRes_.clear();
-    pResPartDeriv_.clear();
     TRes_.clear();
-    TResPartDeriv_.clear();
     phiRes_.clear();
-    phiResPartDeriv_.clear();
 }
 
 void DAResidualSimpleTFoam::calcResiduals(const dictionary& options)
diff --git a/src/adjoint/DAResidual/DAResidualSimpleTFoam.H b/src/adjoint/DAResidual/DAResidualSimpleTFoam.H
index 630a197d..f77a855d 100755
--- a/src/adjoint/DAResidual/DAResidualSimpleTFoam.H
+++ b/src/adjoint/DAResidual/DAResidualSimpleTFoam.H
@@ -33,19 +33,15 @@ protected:
     //@{
     volVectorField& U_;
     volVectorField URes_;
-    volVectorField UResPartDeriv_;
 
     volScalarField& p_;
     volScalarField pRes_;
-    volScalarField pResPartDeriv_;
 
     volScalarField& T_;
     volScalarField TRes_;
-    volScalarField TResPartDeriv_;
 
     surfaceScalarField& phi_;
     surfaceScalarField phiRes_;
-    surfaceScalarField phiResPartDeriv_;
     //@}
 
     /// alpha porosity term
diff --git a/src/adjoint/DAResidual/DAResidualSolidDisplacementFoam.C b/src/adjoint/DAResidual/DAResidualSolidDisplacementFoam.C
index 7f23a810..eabda93a 100755
--- a/src/adjoint/DAResidual/DAResidualSolidDisplacementFoam.C
+++ b/src/adjoint/DAResidual/DAResidualSolidDisplacementFoam.C
@@ -81,7 +81,6 @@ void DAResidualSolidDisplacementFoam::clear()
         in the parent and child classes
     */
     DRes_.clear();
-    DResPartDeriv_.clear();
 }
 
 void DAResidualSolidDisplacementFoam::calcResiduals(const dictionary& options)
diff --git a/src/adjoint/DAResidual/DAResidualSolidDisplacementFoam.H b/src/adjoint/DAResidual/DAResidualSolidDisplacementFoam.H
index d8ba649d..9137b39a 100755
--- a/src/adjoint/DAResidual/DAResidualSolidDisplacementFoam.H
+++ b/src/adjoint/DAResidual/DAResidualSolidDisplacementFoam.H
@@ -32,7 +32,6 @@ protected:
     //@{
     volVectorField& D_;
     volVectorField DRes_;
-    volVectorField DResPartDeriv_;
     //@}
 
     volTensorField& gradD_;
diff --git a/src/adjoint/DAResidual/DAResidualTurboFoam.C b/src/adjoint/DAResidual/DAResidualTurboFoam.C
index 38840505..0c34700d 100755
--- a/src/adjoint/DAResidual/DAResidualTurboFoam.C
+++ b/src/adjoint/DAResidual/DAResidualTurboFoam.C
@@ -70,13 +70,9 @@ void DAResidualTurboFoam::clear()
         in the parent and child classes
     */
     URes_.clear();
-    UResPartDeriv_.clear();
     pRes_.clear();
-    pResPartDeriv_.clear();
     TRes_.clear();
-    TResPartDeriv_.clear();
     phiRes_.clear();
-    phiResPartDeriv_.clear();
 }
 
 void DAResidualTurboFoam::calcResiduals(const dictionary& options)
diff --git a/src/adjoint/DAResidual/DAResidualTurboFoam.H b/src/adjoint/DAResidual/DAResidualTurboFoam.H
index 8495d0b5..9bac991e 100755
--- a/src/adjoint/DAResidual/DAResidualTurboFoam.H
+++ b/src/adjoint/DAResidual/DAResidualTurboFoam.H
@@ -37,19 +37,15 @@ protected:
     //@{
     volVectorField& U_;
     volVectorField URes_;
-    volVectorField UResPartDeriv_;
 
     volScalarField& p_;
     volScalarField pRes_;
-    volScalarField pResPartDeriv_;
 
     volScalarField& T_;
     volScalarField TRes_;
-    volScalarField TResPartDeriv_;
 
     surfaceScalarField& phi_;
     surfaceScalarField phiRes_;
-    surfaceScalarField phiResPartDeriv_;
     //@}
 
     /// thermophysical property
diff --git a/src/adjoint/DASolver/DALaplacianFoam/DALaplacianFoam.C b/src/adjoint/DASolver/DALaplacianFoam/DALaplacianFoam.C
new file mode 100755
index 00000000..68f91c2e
--- /dev/null
+++ b/src/adjoint/DASolver/DALaplacianFoam/DALaplacianFoam.C
@@ -0,0 +1,229 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+\*---------------------------------------------------------------------------*/
+
+#include "DALaplacianFoam.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+defineTypeNameAndDebug(DALaplacianFoam, 0);
+addToRunTimeSelectionTable(DASolver, DALaplacianFoam, dictionary);
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+DALaplacianFoam::DALaplacianFoam(
+    char* argsAll,
+    PyObject* pyOptions)
+    : DASolver(argsAll, pyOptions),
+      TPtr_(nullptr),
+      DTPtr_(nullptr)
+{
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+void DALaplacianFoam::initSolver()
+{
+    /*
+    Description:
+        Initialize variables for DASolver
+    */
+
+    Info << "Initializing fields for DALaplacianFoam" << endl;
+    Time& runTime = runTimePtr_();
+    fvMesh& mesh = meshPtr_();
+#include "createFieldsLaplacian.H"
+#include "createAdjointSolid.H"
+    // initialize checkMesh
+    daCheckMeshPtr_.reset(new DACheckMesh(daOptionPtr_(), runTime, mesh));
+
+    daLinearEqnPtr_.reset(new DALinearEqn(mesh, daOptionPtr_()));
+
+    mode_ = daOptionPtr_->getSubDictOption<word>("unsteadyAdjoint", "mode");
+
+    if (mode_ == "hybridAdjoint")
+    {
+
+        nTimeInstances_ =
+            daOptionPtr_->getSubDictOption<label>("unsteadyAdjoint", "nTimeInstances");
+
+        periodicity_ =
+            daOptionPtr_->getSubDictOption<scalar>("unsteadyAdjoint", "periodicity");
+
+        if (periodicity_ <= 0)
+        {
+            FatalErrorIn("") << "periodicity <= 0!" << abort(FatalError);
+        }
+    }
+    else if (mode_ == "timeAccurateAdjoint")
+    {
+
+        nTimeInstances_ =
+            daOptionPtr_->getSubDictOption<label>("unsteadyAdjoint", "nTimeInstances");
+
+        scalar endTime = runTimePtr_->endTime().value();
+        scalar deltaT = runTimePtr_->deltaTValue();
+        label maxNTimeInstances = round(endTime / deltaT) + 1;
+        if (nTimeInstances_ != maxNTimeInstances)
+        {
+            FatalErrorIn("") << "nTimeInstances in timeAccurateAdjoint is not equal to "
+                             << "the maximal possible value!" << abort(FatalError);
+        }
+    }
+
+    if (mode_ == "hybridAdjoint" || mode_ == "timeAccurateAdjoint")
+    {
+
+        if (nTimeInstances_ <= 0)
+        {
+            FatalErrorIn("") << "nTimeInstances <= 0!" << abort(FatalError);
+        }
+
+        stateAllInstances_.setSize(nTimeInstances_);
+        stateBoundaryAllInstances_.setSize(nTimeInstances_);
+        objFuncsAllInstances_.setSize(nTimeInstances_);
+        runTimeAllInstances_.setSize(nTimeInstances_);
+        runTimeIndexAllInstances_.setSize(nTimeInstances_);
+
+        forAll(stateAllInstances_, idxI)
+        {
+            stateAllInstances_[idxI].setSize(daIndexPtr_->nLocalAdjointStates);
+            stateBoundaryAllInstances_[idxI].setSize(daIndexPtr_->nLocalAdjointBoundaryStates);
+            runTimeAllInstances_[idxI] = 0.0;
+            runTimeIndexAllInstances_[idxI] = 0;
+        }
+    }
+
+    // initialize intermediate variable pointer for mean field calculation
+    daIntmdVarPtr_.reset(new DAIntmdVar(mesh, daOptionPtr_()));
+}
+
+label DALaplacianFoam::solvePrimal(
+    const Vec xvVec,
+    Vec wVec)
+{
+    /*
+    Description:
+        Call the primal solver to get converged state variables
+
+    Input:
+        xvVec: a vector that contains all volume mesh coordinates
+
+    Output:
+        wVec: state variable vector
+    */
+
+#include "createRefsLaplacian.H"
+
+    // change the run status
+    daOptionPtr_->setOption<word>("runStatus", "solvePrimal");
+
+    // first check if we need to change the boundary conditions based on
+    // the primalBC dict in DAOption. NOTE: this will overwrite whatever
+    // boundary conditions defined in the "0" folder
+    dictionary bcDict = daOptionPtr_->getAllOptions().subDict("primalBC");
+    if (bcDict.toc().size() != 0)
+    {
+        Info << "Setting up primal boundary conditions based on pyOptions: " << endl;
+        daFieldPtr_->setPrimalBoundaryConditions();
+    }
+
+    Info << "\nCalculating temperature distribution\n"
+         << endl;
+
+    // deform the mesh based on the xvVec
+    this->pointVec2OFMesh(xvVec);
+
+    // check mesh quality
+    label meshOK = this->checkMesh();
+
+    if (!meshOK)
+    {
+        return 1;
+    }
+
+    // We need to set the mesh moving to false, otherwise we will get V0 not found error.
+    // Need to dig into this issue later
+    // NOTE: we have commented this out. Setting mesh.moving(false) has been done
+    // right after mesh.movePoints() calls.
+    //mesh.moving(false);
+
+    primalMinRes_ = 1e10;
+    label printInterval = daOptionPtr_->getOption<label>("printIntervalUnsteady");
+    label printToScreen = 0;
+    label timeInstanceI = 0;
+    // for time accurate adjoints, we need to save states for Time = 0
+    if (mode_ == "timeAccurateAdjoint")
+    {
+        this->saveTimeInstanceFieldTimeAccurate(timeInstanceI);
+    }
+    // main loop
+    while (this->loop(runTime)) // using simple.loop() will have seg fault in parallel
+    {
+        printToScreen = this->isPrintTime(runTime, printInterval);
+
+        if (printToScreen)
+        {
+            Info << "Time = " << runTime.timeName() << nl << endl;
+        }
+
+        fvScalarMatrix TEqn(
+            fvm::ddt(T)
+            - fvm::laplacian(DT, T));
+
+        // get the solver performance info such as initial
+        // and final residuals
+        SolverPerformance<scalar> solverT = TEqn.solve();
+        this->primalResidualControl<scalar>(solverT, printToScreen, printInterval, "T");
+
+        if (printToScreen)
+        {
+
+            this->printAllObjFuncs();
+
+            if (daOptionPtr_->getOption<label>("debug"))
+            {
+                this->calcPrimalResidualStatistics("print");
+            }
+
+            Info << "ExecutionTime = " << runTime.elapsedCpuTime() << " s"
+                 << "  ClockTime = " << runTime.elapsedClockTime() << " s"
+                 << nl << endl;
+        }
+
+        daIntmdVarPtr_->update();
+
+        runTime.write();
+
+        if (mode_ == "hybridAdjoint")
+        {
+            this->saveTimeInstanceFieldHybrid(timeInstanceI);
+        }
+
+        if (mode_ == "timeAccurateAdjoint")
+        {
+            this->saveTimeInstanceFieldTimeAccurate(timeInstanceI);
+        }
+    }
+
+    this->calcPrimalResidualStatistics("print");
+
+    // primal converged, assign the OpenFoam fields to the state vec wVec
+    this->ofField2StateVec(wVec);
+
+    // write the mesh to files
+    mesh.write();
+
+    Info << "End\n"
+         << endl;
+
+    return 0;
+}
+
+} // End namespace Foam
+
+// ************************************************************************* //
diff --git a/src/adjoint/DASolver/DALaplacianFoam/DALaplacianFoam.H b/src/adjoint/DASolver/DALaplacianFoam/DALaplacianFoam.H
new file mode 100755
index 00000000..63337ffa
--- /dev/null
+++ b/src/adjoint/DASolver/DALaplacianFoam/DALaplacianFoam.H
@@ -0,0 +1,76 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+    Description:
+        Child class for DALaplacianFoam
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef DALaplacianFoam_H
+#define DALaplacianFoam_H
+
+#include "DASolver.H"
+#include "DAIntmdVar.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+/*---------------------------------------------------------------------------*\
+      Class DALaplacianFoam Declaration
+\*---------------------------------------------------------------------------*/
+
+class DALaplacianFoam
+    : public DASolver
+{
+
+protected:
+ 
+    /// temperature field pointer
+    autoPtr<volScalarField> TPtr_;
+
+    /// DT pointer
+    autoPtr<dimensionedScalar> DTPtr_;
+
+    /// DAIntmVar pointer
+    autoPtr<DAIntmdVar> daIntmdVarPtr_;
+
+    /// unsteady mode
+    word mode_ = "None";
+
+
+public:
+    TypeName("DALaplacianFoam");
+    // Constructors
+
+    //- Construct from components
+    DALaplacianFoam(
+        char* argsAll,
+        PyObject* pyOptions);
+
+    //- Destructor
+    virtual ~DALaplacianFoam()
+    {
+    }
+
+    /// initialize fields and variables
+    virtual void initSolver();
+
+    /// solve the primal equations
+    virtual label solvePrimal(
+        const Vec xvVec,
+        Vec wVec);
+};
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //
diff --git a/src/adjoint/DASolver/DALaplacianFoam/createFieldsLaplacian.H b/src/adjoint/DASolver/DALaplacianFoam/createFieldsLaplacian.H
new file mode 100755
index 00000000..1796fc00
--- /dev/null
+++ b/src/adjoint/DASolver/DALaplacianFoam/createFieldsLaplacian.H
@@ -0,0 +1,31 @@
+Info << "Reading field T\n"
+     << endl;
+TPtr_.reset(
+    new volScalarField(
+        IOobject(
+            "T",
+            runTime.timeName(),
+            mesh,
+            IOobject::MUST_READ,
+            IOobject::AUTO_WRITE),
+        mesh));
+
+Info << "Reading transportProperties\n"
+     << endl;
+
+IOdictionary transportProperties(
+    IOobject(
+        "transportProperties",
+        runTime.constant(),
+        mesh,
+        IOobject::MUST_READ,
+        IOobject::NO_WRITE));
+
+Info << "Reading diffusivity DT\n"
+     << endl;
+
+DTPtr_.reset(
+    new dimensionedScalar(
+        "DT",
+        dimViscosity,
+        transportProperties));
\ No newline at end of file
diff --git a/src/adjoint/DASolver/DALaplacianFoam/createRefsLaplacian.H b/src/adjoint/DASolver/DALaplacianFoam/createRefsLaplacian.H
new file mode 100755
index 00000000..c6ac9db3
--- /dev/null
+++ b/src/adjoint/DASolver/DALaplacianFoam/createRefsLaplacian.H
@@ -0,0 +1,11 @@
+Time& runTime = runTimePtr_();
+// reset time to 0
+runTime.setTime(0.0, 0);
+fvMesh& mesh = meshPtr_();
+volScalarField& T = TPtr_();
+dimensionedScalar& DT = DTPtr_();
+
+// create a file to store the objective values
+this->initializeObjFuncHistFilePtr("objFuncTimeSeries");
+
+this->setDAObjFuncList();
diff --git a/src/adjoint/DASolver/DAPimpleFoam/DAPimpleFoam.C b/src/adjoint/DASolver/DAPimpleFoam/DAPimpleFoam.C
new file mode 100755
index 00000000..abcfabc9
--- /dev/null
+++ b/src/adjoint/DASolver/DAPimpleFoam/DAPimpleFoam.C
@@ -0,0 +1,264 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+\*---------------------------------------------------------------------------*/
+
+#include "DAPimpleFoam.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+defineTypeNameAndDebug(DAPimpleFoam, 0);
+addToRunTimeSelectionTable(DASolver, DAPimpleFoam, dictionary);
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+DAPimpleFoam::DAPimpleFoam(
+    char* argsAll,
+    PyObject* pyOptions)
+    : DASolver(argsAll, pyOptions),
+      pimplePtr_(nullptr),
+      pPtr_(nullptr),
+      UPtr_(nullptr),
+      phiPtr_(nullptr),
+      laminarTransportPtr_(nullptr),
+      turbulencePtr_(nullptr),
+      daTurbulenceModelPtr_(nullptr),
+      daIntmdVarPtr_(nullptr),
+      daFvSourcePtr_(nullptr),
+      fvSourcePtr_(nullptr)
+{
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+void DAPimpleFoam::initSolver()
+{
+    /*
+    Description:
+        Initialize variables for DASolver
+    */
+
+    Info << "Initializing fields for DAPimpleFoam" << endl;
+    Time& runTime = runTimePtr_();
+    fvMesh& mesh = meshPtr_();
+#include "createPimpleControlPython.H"
+#include "createFieldsPimple.H"
+#include "createAdjointIncompressible.H"
+    // initialize checkMesh
+    daCheckMeshPtr_.reset(new DACheckMesh(daOptionPtr_(), runTime, mesh));
+
+    daLinearEqnPtr_.reset(new DALinearEqn(mesh, daOptionPtr_()));
+
+    mode_ = daOptionPtr_->getSubDictOption<word>("unsteadyAdjoint", "mode");
+
+    if (mode_ == "hybridAdjoint")
+    {
+
+        nTimeInstances_ =
+            daOptionPtr_->getSubDictOption<label>("unsteadyAdjoint", "nTimeInstances");
+
+        periodicity_ =
+            daOptionPtr_->getSubDictOption<scalar>("unsteadyAdjoint", "periodicity");
+
+        if (periodicity_ <= 0)
+        {
+            FatalErrorIn("") << "periodicity <= 0!" << abort(FatalError);
+        }
+    }
+    else if (mode_ == "timeAccurateAdjoint")
+    {
+
+        nTimeInstances_ =
+            daOptionPtr_->getSubDictOption<label>("unsteadyAdjoint", "nTimeInstances");
+
+        scalar endTime = runTimePtr_->endTime().value();
+        scalar deltaT = runTimePtr_->deltaTValue();
+        label maxNTimeInstances = round(endTime / deltaT) + 1;
+        if (nTimeInstances_ != maxNTimeInstances)
+        {
+            FatalErrorIn("") << "nTimeInstances in timeAccurateAdjoint is not equal to "
+                             << "the maximal possible value!" << abort(FatalError);
+        }
+    }
+
+    if (mode_ == "hybridAdjoint" || mode_ == "timeAccurateAdjoint")
+    {
+
+        if (nTimeInstances_ <= 0)
+        {
+            FatalErrorIn("") << "nTimeInstances <= 0!" << abort(FatalError);
+        }
+
+        stateAllInstances_.setSize(nTimeInstances_);
+        stateBoundaryAllInstances_.setSize(nTimeInstances_);
+        objFuncsAllInstances_.setSize(nTimeInstances_);
+        runTimeAllInstances_.setSize(nTimeInstances_);
+        runTimeIndexAllInstances_.setSize(nTimeInstances_);
+
+        forAll(stateAllInstances_, idxI)
+        {
+            stateAllInstances_[idxI].setSize(daIndexPtr_->nLocalAdjointStates);
+            stateBoundaryAllInstances_[idxI].setSize(daIndexPtr_->nLocalAdjointBoundaryStates);
+            runTimeAllInstances_[idxI] = 0.0;
+            runTimeIndexAllInstances_[idxI] = 0;
+        }
+    }
+
+    // initialize fvSource and the source term
+    const dictionary& allOptions = daOptionPtr_->getAllOptions();
+    if (allOptions.subDict("fvSource").toc().size() != 0)
+    {
+        hasFvSource_ = 1;
+        Info << "Computing fvSource" << endl;
+        word sourceName = allOptions.subDict("fvSource").toc()[0];
+        word fvSourceType = allOptions.subDict("fvSource").subDict(sourceName).getWord("type");
+        daFvSourcePtr_.reset(DAFvSource::New(
+            fvSourceType, mesh, daOptionPtr_(), daModelPtr_(), daIndexPtr_()));
+        daFvSourcePtr_->calcFvSource(fvSource);
+    }
+
+    // initialize intermediate variable pointer for mean field calculation
+    daIntmdVarPtr_.reset(new DAIntmdVar(mesh, daOptionPtr_()));
+}
+
+label DAPimpleFoam::solvePrimal(
+    const Vec xvVec,
+    Vec wVec)
+{
+    /*
+    Description:
+        Call the primal solver to get converged state variables
+
+    Input:
+        xvVec: a vector that contains all volume mesh coordinates
+
+    Output:
+        wVec: state variable vector
+    */
+
+#include "createRefsPimple.H"
+
+    // change the run status
+    daOptionPtr_->setOption<word>("runStatus", "solvePrimal");
+
+    // first check if we need to change the boundary conditions based on
+    // the primalBC dict in DAOption. NOTE: this will overwrite whatever
+    // boundary conditions defined in the "0" folder
+    dictionary bcDict = daOptionPtr_->getAllOptions().subDict("primalBC");
+    if (bcDict.toc().size() != 0)
+    {
+        Info << "Setting up primal boundary conditions based on pyOptions: " << endl;
+        daFieldPtr_->setPrimalBoundaryConditions();
+    }
+
+    // call correctNut, this is equivalent to turbulence->validate();
+    daTurbulenceModelPtr_->updateIntermediateVariables();
+
+    Info << "\nStarting time loop\n"
+         << endl;
+
+    // deform the mesh based on the xvVec
+    this->pointVec2OFMesh(xvVec);
+
+    // check mesh quality
+    label meshOK = this->checkMesh();
+
+    if (!meshOK)
+    {
+        return 1;
+    }
+
+    // We need to set the mesh moving to false, otherwise we will get V0 not found error.
+    // Need to dig into this issue later
+    // NOTE: we have commented this out. Setting mesh.moving(false) has been done
+    // right after mesh.movePoints() calls.
+    //mesh.moving(false);
+
+    primalMinRes_ = 1e10;
+    label printInterval = daOptionPtr_->getOption<label>("printIntervalUnsteady");
+    label printToScreen = 0;
+    label timeInstanceI = 0;
+    // for time accurate adjoints, we need to save states for Time = 0
+    if (mode_ == "timeAccurateAdjoint")
+    {
+        this->saveTimeInstanceFieldTimeAccurate(timeInstanceI);
+    }
+    // main loop
+    while (this->loop(runTime)) // using simple.loop() will have seg fault in parallel
+    {
+        printToScreen = this->isPrintTime(runTime, printInterval);
+
+        if (printToScreen)
+        {
+            Info << "Time = " << runTime.timeName() << nl << endl;
+        }
+
+        // --- Pressure-velocity PIMPLE corrector loop
+        while (pimple.loop())
+        {
+
+#include "UEqnPimple.H"
+
+            // --- Pressure corrector loop
+            while (pimple.correct())
+            {
+#include "pEqnPimple.H"
+            }
+
+            laminarTransport.correct();
+            daTurbulenceModelPtr_->correct();
+        }
+
+        if (printToScreen)
+        {
+#include "CourantNo.H"
+
+            daTurbulenceModelPtr_->printYPlus();
+
+            this->printAllObjFuncs();
+
+            if (daOptionPtr_->getOption<label>("debug"))
+            {
+                this->calcPrimalResidualStatistics("print");
+            }
+
+            Info << "ExecutionTime = " << runTime.elapsedCpuTime() << " s"
+                 << "  ClockTime = " << runTime.elapsedClockTime() << " s"
+                 << nl << endl;
+        }
+
+        daIntmdVarPtr_->update();
+
+        runTime.write();
+
+        if (mode_ == "hybridAdjoint")
+        {
+            this->saveTimeInstanceFieldHybrid(timeInstanceI);
+        }
+
+        if (mode_ == "timeAccurateAdjoint")
+        {
+            this->saveTimeInstanceFieldTimeAccurate(timeInstanceI);
+        }
+    }
+
+    this->calcPrimalResidualStatistics("print");
+
+    // primal converged, assign the OpenFoam fields to the state vec wVec
+    this->ofField2StateVec(wVec);
+
+    // write the mesh to files
+    mesh.write();
+
+    Info << "End\n"
+         << endl;
+
+    return 0;
+}
+
+} // End namespace Foam
+
+// ************************************************************************* //
diff --git a/src/adjoint/DASolver/DAPimpleFoam/DAPimpleFoam.H b/src/adjoint/DASolver/DAPimpleFoam/DAPimpleFoam.H
new file mode 100755
index 00000000..166800bb
--- /dev/null
+++ b/src/adjoint/DASolver/DAPimpleFoam/DAPimpleFoam.H
@@ -0,0 +1,114 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+    Description:
+        Child class for DAPimpleFoam
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef DAPimpleFoam_H
+#define DAPimpleFoam_H
+
+#include "DASolver.H"
+#include "addToRunTimeSelectionTable.H"
+#include "singlePhaseTransportModel.H"
+#include "turbulentTransportModel.H"
+#include "pimpleControl.H"
+#include "DARegDbSinglePhaseTransportModel.H"
+#include "DARegDbTurbulenceModelIncompressible.H"
+#include "DAFvSource.H"
+#include "DAIntmdVar.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+/*---------------------------------------------------------------------------*\
+      Class DAPimpleFoam Declaration
+\*---------------------------------------------------------------------------*/
+
+class DAPimpleFoam
+    : public DASolver
+{
+
+protected:
+    /// pimple pointer
+    autoPtr<pimpleControl> pimplePtr_;
+
+    /// pressure field pointer
+    autoPtr<volScalarField> pPtr_;
+
+    /// velocity field pointer
+    autoPtr<volVectorField> UPtr_;
+
+    /// surface flux field pointer
+    autoPtr<surfaceScalarField> phiPtr_;
+
+    /// laminar transport properties pointer
+    autoPtr<singlePhaseTransportModel> laminarTransportPtr_;
+
+    /// turbulence pointer
+    autoPtr<incompressible::turbulenceModel> turbulencePtr_;
+
+    /// DATurbulenceModel pointer
+    autoPtr<DATurbulenceModel> daTurbulenceModelPtr_;
+
+    /// DAIntmVar pointer
+    autoPtr<DAIntmdVar> daIntmdVarPtr_;
+
+    /// DASource pointer
+    autoPtr<DAFvSource> daFvSourcePtr_;
+
+    /// fvSource term
+    autoPtr<volVectorField> fvSourcePtr_;
+
+    /// whether to have fvSource term
+    label hasFvSource_ = 0;
+
+    /// continuity error
+    scalar cumulativeContErr_ = 0.0;
+
+    /// pressure referefence cell id
+    label pRefCell_ = 0;
+
+    /// pressure reference value
+    scalar pRefValue_ = 0.0;
+
+    /// whether the hybrid adjoint or time accurate adjoint is active
+    word mode_ = "None";
+
+public:
+    TypeName("DAPimpleFoam");
+    // Constructors
+
+    //- Construct from components
+    DAPimpleFoam(
+        char* argsAll,
+        PyObject* pyOptions);
+
+    //- Destructor
+    virtual ~DAPimpleFoam()
+    {
+    }
+
+    /// initialize fields and variables
+    virtual void initSolver();
+
+    /// solve the primal equations
+    virtual label solvePrimal(
+        const Vec xvVec,
+        Vec wVec);
+};
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //
diff --git a/src/adjoint/DASolver/DAPimpleFoam/UEqnPimple.H b/src/adjoint/DASolver/DAPimpleFoam/UEqnPimple.H
new file mode 100755
index 00000000..54b2bf69
--- /dev/null
+++ b/src/adjoint/DASolver/DAPimpleFoam/UEqnPimple.H
@@ -0,0 +1,26 @@
+// Solve the Momentum equation
+
+if (hasFvSource_)
+{
+    // update the actuator source term
+    daFvSourcePtr_->calcFvSource(fvSource);
+}
+
+tmp<fvVectorMatrix> tUEqn(
+    fvm::ddt(U)
+    + fvm::div(phi, U)
+    + turbulencePtr_->divDevReff(U)
+    - fvSource);
+
+fvVectorMatrix& UEqn = tUEqn.ref();
+
+UEqn.relax();
+
+if (pimple.momentumPredictor())
+{
+    // get the solver performance info such as initial
+    // and final residuals
+    SolverPerformance<vector> solverU = solve(UEqn == -fvc::grad(p));
+
+    this->primalResidualControl<vector>(solverU, printToScreen, printInterval, "U");
+}
diff --git a/src/adjoint/DASolver/DAPimpleFoam/createFieldsPimple.H b/src/adjoint/DASolver/DAPimpleFoam/createFieldsPimple.H
new file mode 100755
index 00000000..dd46a629
--- /dev/null
+++ b/src/adjoint/DASolver/DAPimpleFoam/createFieldsPimple.H
@@ -0,0 +1,52 @@
+Info << "Reading field p\n"
+     << endl;
+pPtr_.reset(
+    new volScalarField(
+        IOobject(
+            "p",
+            runTime.timeName(),
+            mesh,
+            IOobject::MUST_READ,
+            IOobject::AUTO_WRITE),
+        mesh));
+volScalarField& p = pPtr_();
+
+Info << "Reading field U\n"
+     << endl;
+UPtr_.reset(
+    new volVectorField(
+        IOobject(
+            "U",
+            runTime.timeName(),
+            mesh,
+            IOobject::MUST_READ,
+            IOobject::AUTO_WRITE),
+        mesh));
+volVectorField& U = UPtr_();
+
+#include "createPhiPython.H"
+
+// actuator related stuff
+Info << "Creating source term. " << endl;
+fvSourcePtr_.reset(
+    new volVectorField(
+        IOobject(
+            "fvSource",
+            runTime.timeName(),
+            mesh,
+            IOobject::NO_READ,
+            IOobject::AUTO_WRITE),
+        mesh,
+        dimensionedVector("fvSource", dimensionSet(0, 1, -2, 0, 0, 0, 0), vector::zero),
+        zeroGradientFvPatchField<vector>::typeName));
+volVectorField& fvSource = fvSourcePtr_();
+
+setRefCell(p, pimple.dict(), pRefCell_, pRefValue_);
+mesh.setFluxRequired(p.name());
+
+laminarTransportPtr_.reset(
+    new singlePhaseTransportModel(U, phi));
+singlePhaseTransportModel& laminarTransport = laminarTransportPtr_();
+
+turbulencePtr_.reset(
+    incompressible::turbulenceModel::New(U, phi, laminarTransport));
diff --git a/src/adjoint/DASolver/DAPimpleFoam/createRefsPimple.H b/src/adjoint/DASolver/DAPimpleFoam/createRefsPimple.H
new file mode 100755
index 00000000..279cbe7b
--- /dev/null
+++ b/src/adjoint/DASolver/DAPimpleFoam/createRefsPimple.H
@@ -0,0 +1,18 @@
+Time& runTime = runTimePtr_();
+// reset time to 0
+runTime.setTime(0.0, 0);
+fvMesh& mesh = meshPtr_();
+pimpleControl& pimple = pimplePtr_();
+volScalarField& p = pPtr_();
+volVectorField& U = UPtr_();
+surfaceScalarField& phi = phiPtr_();
+singlePhaseTransportModel& laminarTransport = laminarTransportPtr_();
+scalar& cumulativeContErr = cumulativeContErr_;
+label& pRefCell = pRefCell_;
+scalar& pRefValue = pRefValue_;
+volVectorField& fvSource = fvSourcePtr_();
+
+// create a file to store the objective values
+this->initializeObjFuncHistFilePtr("objFuncTimeSeries");
+
+this->setDAObjFuncList();
diff --git a/src/adjoint/DASolver/DAPimpleFoam/pEqnPimple.H b/src/adjoint/DASolver/DAPimpleFoam/pEqnPimple.H
new file mode 100755
index 00000000..121eede6
--- /dev/null
+++ b/src/adjoint/DASolver/DAPimpleFoam/pEqnPimple.H
@@ -0,0 +1,55 @@
+volScalarField rAU(1.0 / UEqn.A());
+volVectorField HbyA(constrainHbyA(rAU* UEqn.H(), U, p));
+surfaceScalarField phiHbyA(
+    "phiHbyA",
+    fvc::flux(HbyA)
+        + fvc::interpolate(rAU) * fvc::ddtCorr(U, phi));
+
+adjustPhi(phiHbyA, U, p);
+
+tmp<volScalarField> rAtU(rAU);
+
+if (pimple.consistent())
+{
+    rAtU = 1.0 / max(1.0 / rAU - UEqn.H1(), 0.1 / rAU);
+    phiHbyA +=
+        fvc::interpolate(rAtU() - rAU) * fvc::snGrad(p) * mesh.magSf();
+    HbyA -= (rAU - rAtU()) * fvc::grad(p);
+}
+
+if (pimple.nCorrPISO() <= 1)
+{
+    tUEqn.clear();
+}
+
+// Non-orthogonal pressure corrector loop
+while (pimple.correctNonOrthogonal())
+{
+    // Pressure corrector
+    fvScalarMatrix pEqn(
+        fvm::laplacian(rAtU(), p) == fvc::div(phiHbyA));
+
+    pEqn.setReference(pRefCell, pRefValue);
+
+    // get the solver performance info such as initial
+    // and final residuals
+    SolverPerformance<scalar> solverP = pEqn.solve(mesh.solver(p.select(pimple.finalInnerIter())));
+
+    this->primalResidualControl<scalar>(solverP, printToScreen, printInterval, "p");
+
+    if (pimple.finalNonOrthogonalIter())
+    {
+        phi = phiHbyA - pEqn.flux();
+    }
+}
+
+if (printToScreen)
+{
+#include "continuityErrsPython.H"
+}
+
+// Explicitly relax pressure for momentum corrector
+p.relax();
+
+U = HbyA - rAtU() * fvc::grad(p);
+U.correctBoundaryConditions();
diff --git a/src/adjoint/DASolver/DAPisoFoam/DAPisoFoam.C b/src/adjoint/DASolver/DAPisoFoam/DAPisoFoam.C
index ee8de955..e167d922 100755
--- a/src/adjoint/DASolver/DAPisoFoam/DAPisoFoam.C
+++ b/src/adjoint/DASolver/DAPisoFoam/DAPisoFoam.C
@@ -52,41 +52,59 @@ void DAPisoFoam::initSolver()
 
     daLinearEqnPtr_.reset(new DALinearEqn(mesh, daOptionPtr_()));
 
-    label active = daOptionPtr_->getSubDictOption<label>("hybridAdjoint", "active");
+    mode_ = daOptionPtr_->getSubDictOption<word>("unsteadyAdjoint", "mode");
 
-    nTimeInstances_ =
-        daOptionPtr_->getSubDictOption<label>("hybridAdjoint", "nTimeInstances");
+    if (mode_ == "hybridAdjoint")
+    {
 
-    periodicity_ =
-        daOptionPtr_->getSubDictOption<scalar>("hybridAdjoint", "periodicity");
+        nTimeInstances_ =
+            daOptionPtr_->getSubDictOption<label>("unsteadyAdjoint", "nTimeInstances");
 
-    if (!active)
-    {
-        FatalErrorIn("hybridAdjoint") << "active is False!" << abort(FatalError);
-    }
+        periodicity_ =
+            daOptionPtr_->getSubDictOption<scalar>("unsteadyAdjoint", "periodicity");
 
-    if (periodicity_ <= 0)
+        if (periodicity_ <= 0)
+        {
+            FatalErrorIn("") << "periodicity <= 0!" << abort(FatalError);
+        }
+    }
+    else if (mode_ == "timeAccurateAdjoint")
     {
-        FatalErrorIn("hybridAdjoint") << "periodicity <= 0!" << abort(FatalError);
+
+        nTimeInstances_ =
+            daOptionPtr_->getSubDictOption<label>("unsteadyAdjoint", "nTimeInstances");
+
+        scalar endTime = runTimePtr_->endTime().value();
+        scalar deltaT = runTimePtr_->deltaTValue();
+        label maxNTimeInstances = round(endTime / deltaT) + 1;
+        if (nTimeInstances_ != maxNTimeInstances)
+        {
+            FatalErrorIn("") << "nTimeInstances in timeAccurateAdjoint is not equal to "
+                             << "the maximal possible value!" << abort(FatalError);
+        }
     }
 
-    if (nTimeInstances_ <= 0)
+    if (mode_ == "hybridAdjoint" || mode_ == "timeAccurateAdjoint")
     {
-        FatalErrorIn("hybridAdjoint") << "nTimeInstances <= 0!" << abort(FatalError);
-    }
 
-    stateAllInstances_.setSize(nTimeInstances_);
-    stateBounaryAllInstances_.setSize(nTimeInstances_);
-    objFuncsAllInstances_.setSize(nTimeInstances_);
-    runTimeAllInstances_.setSize(nTimeInstances_);
-    runTimeIndexAllInstances_.setSize(nTimeInstances_);
+        if (nTimeInstances_ <= 0)
+        {
+            FatalErrorIn("") << "nTimeInstances <= 0!" << abort(FatalError);
+        }
+
+        stateAllInstances_.setSize(nTimeInstances_);
+        stateBoundaryAllInstances_.setSize(nTimeInstances_);
+        objFuncsAllInstances_.setSize(nTimeInstances_);
+        runTimeAllInstances_.setSize(nTimeInstances_);
+        runTimeIndexAllInstances_.setSize(nTimeInstances_);
 
-    forAll(stateAllInstances_, idxI)
-    {
-        stateAllInstances_[idxI].setSize(daIndexPtr_->nLocalAdjointStates);
-        stateBounaryAllInstances_[idxI].setSize(daIndexPtr_->nLocalAdjointBoundaryStates);
-        runTimeAllInstances_[idxI] = 0.0;
-        runTimeIndexAllInstances_[idxI] = 0.0;
+        forAll(stateAllInstances_, idxI)
+        {
+            stateAllInstances_[idxI].setSize(daIndexPtr_->nLocalAdjointStates);
+            stateBoundaryAllInstances_[idxI].setSize(daIndexPtr_->nLocalAdjointBoundaryStates);
+            runTimeAllInstances_[idxI] = 0.0;
+            runTimeIndexAllInstances_[idxI] = 0;
+        }
     }
 
     // initialize fvSource and the source term
@@ -104,7 +122,6 @@ void DAPisoFoam::initSolver()
 
     // initialize intermediate variable pointer for mean field calculation
     daIntmdVarPtr_.reset(new DAIntmdVar(mesh, daOptionPtr_()));
-
 }
 
 label DAPisoFoam::solvePrimal(
@@ -156,12 +173,20 @@ label DAPisoFoam::solvePrimal(
 
     // We need to set the mesh moving to false, otherwise we will get V0 not found error.
     // Need to dig into this issue later
-    mesh.moving(false);
+    // NOTE: we have commented this out. Setting mesh.moving(false) has been done
+    // right after mesh.movePoints() calls.
+    //mesh.moving(false);
 
     primalMinRes_ = 1e10;
     label printInterval = daOptionPtr_->getOption<label>("printIntervalUnsteady");
     label printToScreen = 0;
     label timeInstanceI = 0;
+    // for time accurate adjoints, we need to save states for Time = 0
+    if (mode_ == "timeAccurateAdjoint")
+    {
+        this->saveTimeInstanceFieldTimeAccurate(timeInstanceI);
+    }
+    // main loop
     while (this->loop(runTime)) // using simple.loop() will have seg fault in parallel
     {
         printToScreen = this->isPrintTime(runTime, printInterval);
@@ -193,6 +218,11 @@ label DAPisoFoam::solvePrimal(
 
             this->printAllObjFuncs();
 
+            if (daOptionPtr_->getOption<label>("debug"))
+            {
+                this->calcPrimalResidualStatistics("print");
+            }
+
             Info << "ExecutionTime = " << runTime.elapsedCpuTime() << " s"
                  << "  ClockTime = " << runTime.elapsedClockTime() << " s"
                  << nl << endl;
@@ -202,7 +232,15 @@ label DAPisoFoam::solvePrimal(
 
         runTime.write();
 
-        this->saveTimeInstanceField(timeInstanceI);
+        if (mode_ == "hybridAdjoint")
+        {
+            this->saveTimeInstanceFieldHybrid(timeInstanceI);
+        }
+
+        if (mode_ == "timeAccurateAdjoint")
+        {
+            this->saveTimeInstanceFieldTimeAccurate(timeInstanceI);
+        }
     }
 
     this->calcPrimalResidualStatistics("print");
@@ -219,94 +257,6 @@ label DAPisoFoam::solvePrimal(
     return 0;
 }
 
-void DAPisoFoam::saveTimeInstanceField(label& timeInstanceI)
-{
-    /*
-    Description:
-        Save primal variable to time instance list for unsteady adjoint
-        Here we save the last nTimeInstances snapshots
-    */
-
-    scalar endTime = runTimePtr_->endTime().value();
-    scalar t = runTimePtr_->timeOutputValue();
-    scalar instanceStart =
-        endTime - periodicity_ / nTimeInstances_ * (nTimeInstances_ - 1 - timeInstanceI);
-
-    // the 2nd condition is for t=9.999999999999 scenario)
-    if (t > instanceStart || fabs(t - endTime) < 1e-8)
-    {
-        Info << "Saving time instance " << timeInstanceI << " at Time = " << t << endl;
-
-        // save fields
-        daFieldPtr_->ofField2List(
-            stateAllInstances_[timeInstanceI],
-            stateBounaryAllInstances_[timeInstanceI]);
-
-        // save objective functions
-        forAll(daOptionPtr_->getAllOptions().subDict("objFunc").toc(), idxI)
-        {
-            word objFuncName = daOptionPtr_->getAllOptions().subDict("objFunc").toc()[idxI];
-            scalar objFuncVal = this->getObjFuncValue(objFuncName);
-            objFuncsAllInstances_[timeInstanceI].set(objFuncName, objFuncVal);
-        }
-
-        // save runTime
-        runTimeAllInstances_[timeInstanceI] = t;
-        runTimeIndexAllInstances_[timeInstanceI] = runTimePtr_->timeIndex();
-
-        if (daOptionPtr_->getOption<label>("debug"))
-        {
-            this->calcPrimalResidualStatistics("print");
-        }
-
-        timeInstanceI++;
-    }
-    return;
-}
-
-void DAPisoFoam::setTimeInstanceField(const label instanceI)
-{
-    /*
-    Description:
-        Assign primal variables based on the current time instance
-        If unsteady adjoint solvers are used, this virtual function should be 
-        implemented in a child class, otherwise, return error if called
-    */
-
-    Info << "Setting fields for time instance " << instanceI << endl;
-
-    // set fields
-    daFieldPtr_->list2OFField(
-        stateAllInstances_[instanceI],
-        stateBounaryAllInstances_[instanceI]);
-
-    // set run time
-    runTimePtr_->setTime(runTimeAllInstances_[instanceI], runTimeIndexAllInstances_[instanceI]);
-
-    // We need to call correctBC multiple times to reproduce
-    // the exact residual for mulitpoint, this is needed for some boundary conditions
-    // and intermediate variables (e.g., U for inletOutlet, nut with wall functions)
-    for (label i = 0; i < 10; i++)
-    {
-        daResidualPtr_->correctBoundaryConditions();
-        daResidualPtr_->updateIntermediateVariables();
-        daModelPtr_->correctBoundaryConditions();
-        daModelPtr_->updateIntermediateVariables();
-    }
-}
-
-scalar DAPisoFoam::getTimeInstanceObjFunc(
-    const label instanceI,
-    const word objFuncName)
-{
-    /*
-    Description:
-        Return the value of objective function at the given time instance and name
-    */
-
-    return objFuncsAllInstances_[instanceI].getScalar(objFuncName);
-}
-
 } // End namespace Foam
 
 // ************************************************************************* //
diff --git a/src/adjoint/DASolver/DAPisoFoam/DAPisoFoam.H b/src/adjoint/DASolver/DAPisoFoam/DAPisoFoam.H
index c98f1653..c4b57bca 100755
--- a/src/adjoint/DASolver/DAPisoFoam/DAPisoFoam.H
+++ b/src/adjoint/DASolver/DAPisoFoam/DAPisoFoam.H
@@ -62,7 +62,7 @@ protected:
     /// DASource pointer
     autoPtr<DAFvSource> daFvSourcePtr_;
 
-    /// fvSource term 
+    /// fvSource term
     autoPtr<volVectorField> fvSourcePtr_;
 
     /// whether to have fvSource term
@@ -77,29 +77,8 @@ protected:
     /// pressure reference value
     scalar pRefValue_ = 0.0;
 
-    /// state variable list for all instances
-    List<List<scalar>> stateAllInstances_;
-
-    /// state boundary variable list for all instances
-    List<List<scalar>> stateBounaryAllInstances_;
-
-    /// objective function for all instances
-    List<dictionary> objFuncsAllInstances_;
-
-    /// the runtime value for all instances
-    List<scalar> runTimeAllInstances_;
-
-    /// the runtime index for all instances
-    List<label> runTimeIndexAllInstances_;
-
-    /// number of time instances for hybird adjoint
-    label nTimeInstances_;
-
-    /// periodicity of oscillating flow variables
-    scalar periodicity_;
-
-    /// save primal variable to time instance list for unsteady adjoint
-    void saveTimeInstanceField(label& timeInstanceI);
+    /// whether the hybrid adjoint or time accurate adjoint is active
+    word mode_ = "None";
 
 public:
     TypeName("DAPisoFoam");
@@ -122,14 +101,6 @@ public:
     virtual label solvePrimal(
         const Vec xvVec,
         Vec wVec);
-
-    /// assign primal variables based on the current time instance
-    virtual void setTimeInstanceField(const label instanceI);
-
-    /// return the value of objective function at the given time instance and name
-    virtual scalar getTimeInstanceObjFunc(
-        const label instanceI,
-        const word objFuncName);
 };
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
diff --git a/src/adjoint/DASolver/DAPisoFoam/createRefsPiso.H b/src/adjoint/DASolver/DAPisoFoam/createRefsPiso.H
index 3435fbe9..b25dadad 100755
--- a/src/adjoint/DASolver/DAPisoFoam/createRefsPiso.H
+++ b/src/adjoint/DASolver/DAPisoFoam/createRefsPiso.H
@@ -13,6 +13,6 @@ scalar& pRefValue = pRefValue_;
 volVectorField& fvSource = fvSourcePtr_();
 
 // create a file to store the objective values
-this->initializeObjFuncHistFilePtr("objFuncHist");
+this->initializeObjFuncHistFilePtr("objFuncTimeSeries");
 
 this->setDAObjFuncList();
diff --git a/src/adjoint/DASolver/DAPisoFoam/pEqnPiso.H b/src/adjoint/DASolver/DAPisoFoam/pEqnPiso.H
index d48983e5..b69b0e98 100755
--- a/src/adjoint/DASolver/DAPisoFoam/pEqnPiso.H
+++ b/src/adjoint/DASolver/DAPisoFoam/pEqnPiso.H
@@ -1,6 +1,9 @@
 volScalarField rAU(1.0 / UEqn.A());
 volVectorField HbyA(constrainHbyA(rAU* UEqn.H(), U, p));
-surfaceScalarField phiHbyA("phiHbyA", fvc::flux(HbyA));
+surfaceScalarField phiHbyA(
+    "phiHbyA",
+    fvc::flux(HbyA)
+        + fvc::interpolate(rAU) * fvc::ddtCorr(U, phi));
 
 adjustPhi(phiHbyA, U, p);
 
diff --git a/src/adjoint/DASolver/DARhoSimpleCFoam/createRefsRhoSimpleC.H b/src/adjoint/DASolver/DARhoSimpleCFoam/createRefsRhoSimpleC.H
index 2164f077..656176bb 100755
--- a/src/adjoint/DASolver/DARhoSimpleCFoam/createRefsRhoSimpleC.H
+++ b/src/adjoint/DASolver/DARhoSimpleCFoam/createRefsRhoSimpleC.H
@@ -15,6 +15,6 @@ const volScalarField& psi = thermo.psi();
 const dictionary& allOptions = daOptionPtr_->getAllOptions();
 
 // create a file to store the objective values
-this->initializeObjFuncHistFilePtr("objFuncHist");
+this->initializeObjFuncHistFilePtr("objFuncTimeSeries");
 
 this->setDAObjFuncList();
diff --git a/src/adjoint/DASolver/DARhoSimpleFoam/createRefsRhoSimple.H b/src/adjoint/DASolver/DARhoSimpleFoam/createRefsRhoSimple.H
index 01c0984f..34deb786 100755
--- a/src/adjoint/DASolver/DARhoSimpleFoam/createRefsRhoSimple.H
+++ b/src/adjoint/DASolver/DARhoSimpleFoam/createRefsRhoSimple.H
@@ -18,6 +18,6 @@ volScalarField& fvSourceEnergy = fvSourceEnergyPtr_();
 IOMRFZoneList& MRF = MRFPtr_();
 
 // create a file to store the objective values
-this->initializeObjFuncHistFilePtr("objFuncHist");
+this->initializeObjFuncHistFilePtr("objFuncTimeSeries");
 
 this->setDAObjFuncList();
diff --git a/src/adjoint/DASolver/DAScalarTransportFoam/DAScalarTransportFoam.C b/src/adjoint/DASolver/DAScalarTransportFoam/DAScalarTransportFoam.C
new file mode 100755
index 00000000..5489f314
--- /dev/null
+++ b/src/adjoint/DASolver/DAScalarTransportFoam/DAScalarTransportFoam.C
@@ -0,0 +1,234 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+\*---------------------------------------------------------------------------*/
+
+#include "DAScalarTransportFoam.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+defineTypeNameAndDebug(DAScalarTransportFoam, 0);
+addToRunTimeSelectionTable(DASolver, DAScalarTransportFoam, dictionary);
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+DAScalarTransportFoam::DAScalarTransportFoam(
+    char* argsAll,
+    PyObject* pyOptions)
+    : DASolver(argsAll, pyOptions),
+      TPtr_(nullptr),
+      UPtr_(nullptr),
+      phiPtr_(nullptr),
+      DTPtr_(nullptr)
+{
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+void DAScalarTransportFoam::initSolver()
+{
+    /*
+    Description:
+        Initialize variables for DASolver
+    */
+
+    Info << "Initializing fields for DAScalarTransportFoam" << endl;
+    Time& runTime = runTimePtr_();
+    fvMesh& mesh = meshPtr_();
+#include "createFieldsScalarTransport.H"
+#include "createAdjointSolid.H"
+    // initialize checkMesh
+    daCheckMeshPtr_.reset(new DACheckMesh(daOptionPtr_(), runTime, mesh));
+
+    daLinearEqnPtr_.reset(new DALinearEqn(mesh, daOptionPtr_()));
+
+    mode_ = daOptionPtr_->getSubDictOption<word>("unsteadyAdjoint", "mode");
+
+    if (mode_ == "hybridAdjoint")
+    {
+
+        nTimeInstances_ =
+            daOptionPtr_->getSubDictOption<label>("unsteadyAdjoint", "nTimeInstances");
+
+        periodicity_ =
+            daOptionPtr_->getSubDictOption<scalar>("unsteadyAdjoint", "periodicity");
+
+        if (periodicity_ <= 0)
+        {
+            FatalErrorIn("") << "periodicity <= 0!" << abort(FatalError);
+        }
+    }
+    else if (mode_ == "timeAccurateAdjoint")
+    {
+
+        nTimeInstances_ =
+            daOptionPtr_->getSubDictOption<label>("unsteadyAdjoint", "nTimeInstances");
+
+        scalar endTime = runTimePtr_->endTime().value();
+        scalar deltaT = runTimePtr_->deltaTValue();
+        label maxNTimeInstances = round(endTime / deltaT) + 1;
+        if (nTimeInstances_ != maxNTimeInstances)
+        {
+            FatalErrorIn("") << "nTimeInstances in timeAccurateAdjoint is not equal to "
+                             << "the maximal possible value!" << abort(FatalError);
+        }
+    }
+
+    if (mode_ == "hybridAdjoint" || mode_ == "timeAccurateAdjoint")
+    {
+
+        if (nTimeInstances_ <= 0)
+        {
+            FatalErrorIn("") << "nTimeInstances <= 0!" << abort(FatalError);
+        }
+
+        stateAllInstances_.setSize(nTimeInstances_);
+        stateBoundaryAllInstances_.setSize(nTimeInstances_);
+        objFuncsAllInstances_.setSize(nTimeInstances_);
+        runTimeAllInstances_.setSize(nTimeInstances_);
+        runTimeIndexAllInstances_.setSize(nTimeInstances_);
+
+        forAll(stateAllInstances_, idxI)
+        {
+            stateAllInstances_[idxI].setSize(daIndexPtr_->nLocalAdjointStates);
+            stateBoundaryAllInstances_[idxI].setSize(daIndexPtr_->nLocalAdjointBoundaryStates);
+            runTimeAllInstances_[idxI] = 0.0;
+            runTimeIndexAllInstances_[idxI] = 0;
+        }
+    }
+
+    // initialize intermediate variable pointer for mean field calculation
+    daIntmdVarPtr_.reset(new DAIntmdVar(mesh, daOptionPtr_()));
+}
+
+label DAScalarTransportFoam::solvePrimal(
+    const Vec xvVec,
+    Vec wVec)
+{
+    /*
+    Description:
+        Call the primal solver to get converged state variables
+
+    Input:
+        xvVec: a vector that contains all volume mesh coordinates
+
+    Output:
+        wVec: state variable vector
+    */
+
+#include "createRefsScalarTransport.H"
+
+    // change the run status
+    daOptionPtr_->setOption<word>("runStatus", "solvePrimal");
+
+    // first check if we need to change the boundary conditions based on
+    // the primalBC dict in DAOption. NOTE: this will overwrite whatever
+    // boundary conditions defined in the "0" folder
+    dictionary bcDict = daOptionPtr_->getAllOptions().subDict("primalBC");
+    if (bcDict.toc().size() != 0)
+    {
+        Info << "Setting up primal boundary conditions based on pyOptions: " << endl;
+        daFieldPtr_->setPrimalBoundaryConditions();
+    }
+
+    Info << "\nCalculating temperature distribution\n"
+         << endl;
+
+    // deform the mesh based on the xvVec
+    this->pointVec2OFMesh(xvVec);
+
+    // check mesh quality
+    label meshOK = this->checkMesh();
+
+    if (!meshOK)
+    {
+        return 1;
+    }
+
+    // We need to set the mesh moving to false, otherwise we will get V0 not found error.
+    // Need to dig into this issue later
+    // NOTE: we have commented this out. Setting mesh.moving(false) has been done
+    // right after mesh.movePoints() calls.
+    //mesh.moving(false);
+
+    primalMinRes_ = 1e10;
+    label printInterval = daOptionPtr_->getOption<label>("printIntervalUnsteady");
+    label printToScreen = 0;
+    label timeInstanceI = 0;
+    // for time accurate adjoints, we need to save states for Time = 0
+    if (mode_ == "timeAccurateAdjoint")
+    {
+        this->saveTimeInstanceFieldTimeAccurate(timeInstanceI);
+    }
+    // main loop
+    while (this->loop(runTime)) // using simple.loop() will have seg fault in parallel
+    {
+        printToScreen = this->isPrintTime(runTime, printInterval);
+
+        if (printToScreen)
+        {
+            Info << "Time = " << runTime.timeName() << nl << endl;
+        }
+
+        fvScalarMatrix TEqn(
+            fvm::ddt(T)
+            + fvm::div(phi, T)
+            - fvm::laplacian(DT, T));
+
+        TEqn.relax();
+
+        // get the solver performance info such as initial
+        // and final residuals
+        SolverPerformance<scalar> solverT = TEqn.solve();
+        this->primalResidualControl<scalar>(solverT, printToScreen, printInterval, "T");
+
+        if (printToScreen)
+        {
+
+            this->printAllObjFuncs();
+
+            if (daOptionPtr_->getOption<label>("debug"))
+            {
+                this->calcPrimalResidualStatistics("print");
+            }
+
+            Info << "ExecutionTime = " << runTime.elapsedCpuTime() << " s"
+                 << "  ClockTime = " << runTime.elapsedClockTime() << " s"
+                 << nl << endl;
+        }
+
+        daIntmdVarPtr_->update();
+
+        runTime.write();
+
+        if (mode_ == "hybridAdjoint")
+        {
+            this->saveTimeInstanceFieldHybrid(timeInstanceI);
+        }
+
+        if (mode_ == "timeAccurateAdjoint")
+        {
+            this->saveTimeInstanceFieldTimeAccurate(timeInstanceI);
+        }
+    }
+
+    this->calcPrimalResidualStatistics("print");
+
+    // primal converged, assign the OpenFoam fields to the state vec wVec
+    this->ofField2StateVec(wVec);
+
+    // write the mesh to files
+    mesh.write();
+
+    Info << "End\n"
+         << endl;
+
+    return 0;
+}
+
+} // End namespace Foam
+
+// ************************************************************************* //
diff --git a/src/adjoint/DASolver/DAScalarTransportFoam/DAScalarTransportFoam.H b/src/adjoint/DASolver/DAScalarTransportFoam/DAScalarTransportFoam.H
new file mode 100755
index 00000000..c2aee8f5
--- /dev/null
+++ b/src/adjoint/DASolver/DAScalarTransportFoam/DAScalarTransportFoam.H
@@ -0,0 +1,82 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+    Description:
+        Child class for DAScalarTransportFoam
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef DAScalarTransportFoam_H
+#define DAScalarTransportFoam_H
+
+#include "DASolver.H"
+#include "DAIntmdVar.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+/*---------------------------------------------------------------------------*\
+      Class DAScalarTransportFoam Declaration
+\*---------------------------------------------------------------------------*/
+
+class DAScalarTransportFoam
+    : public DASolver
+{
+
+protected:
+ 
+    /// temperature field pointer
+    autoPtr<volScalarField> TPtr_;
+
+    /// velocity field pointer
+    autoPtr<volVectorField> UPtr_;
+
+    /// flux field pointer
+    autoPtr<surfaceScalarField> phiPtr_;
+
+    /// DT pointer
+    autoPtr<dimensionedScalar> DTPtr_;
+
+    /// DAIntmVar pointer
+    autoPtr<DAIntmdVar> daIntmdVarPtr_;
+
+    /// unsteady mode
+    word mode_ = "None";
+
+
+public:
+    TypeName("DAScalarTransportFoam");
+    // Constructors
+
+    //- Construct from components
+    DAScalarTransportFoam(
+        char* argsAll,
+        PyObject* pyOptions);
+
+    //- Destructor
+    virtual ~DAScalarTransportFoam()
+    {
+    }
+
+    /// initialize fields and variables
+    virtual void initSolver();
+
+    /// solve the primal equations
+    virtual label solvePrimal(
+        const Vec xvVec,
+        Vec wVec);
+};
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //
diff --git a/src/adjoint/DASolver/DAScalarTransportFoam/createFieldsScalarTransport.H b/src/adjoint/DASolver/DAScalarTransportFoam/createFieldsScalarTransport.H
new file mode 100755
index 00000000..25c9b213
--- /dev/null
+++ b/src/adjoint/DASolver/DAScalarTransportFoam/createFieldsScalarTransport.H
@@ -0,0 +1,58 @@
+Info << "Reading field T\n"
+     << endl;
+TPtr_.reset(
+    new volScalarField(
+        IOobject(
+            "T",
+            runTime.timeName(),
+            mesh,
+            IOobject::MUST_READ,
+            IOobject::AUTO_WRITE),
+        mesh));
+
+Info << "Reading field U\n"
+     << endl;
+
+UPtr_.reset(
+    new volVectorField(
+        IOobject(
+            "U",
+            runTime.timeName(),
+            mesh,
+            IOobject::MUST_READ,
+            IOobject::AUTO_WRITE),
+        mesh));
+volVectorField& U = UPtr_();
+
+Info << "Reading transportProperties\n"
+     << endl;
+
+IOdictionary transportProperties(
+    IOobject(
+        "transportProperties",
+        runTime.constant(),
+        mesh,
+        IOobject::MUST_READ,
+        IOobject::NO_WRITE));
+
+Info << "Reading diffusivity DT\n"
+     << endl;
+
+DTPtr_.reset(
+    new dimensionedScalar(
+        "DT",
+        dimViscosity,
+        transportProperties));
+
+Info << "Reading/calculating face flux field phi\n"
+     << endl;
+
+phiPtr_.reset(
+    new surfaceScalarField(
+        IOobject(
+            "phi",
+            runTime.timeName(),
+            mesh,
+            IOobject::READ_IF_PRESENT,
+            IOobject::AUTO_WRITE),
+        fvc::flux(U)));
\ No newline at end of file
diff --git a/src/adjoint/DASolver/DAScalarTransportFoam/createRefsScalarTransport.H b/src/adjoint/DASolver/DAScalarTransportFoam/createRefsScalarTransport.H
new file mode 100755
index 00000000..e17f9cb3
--- /dev/null
+++ b/src/adjoint/DASolver/DAScalarTransportFoam/createRefsScalarTransport.H
@@ -0,0 +1,12 @@
+Time& runTime = runTimePtr_();
+// reset time to 0
+runTime.setTime(0.0, 0);
+fvMesh& mesh = meshPtr_();
+volScalarField& T = TPtr_();
+surfaceScalarField& phi = phiPtr_();
+dimensionedScalar& DT = DTPtr_();
+
+// create a file to store the objective values
+this->initializeObjFuncHistFilePtr("objFuncTimeSeries");
+
+this->setDAObjFuncList();
diff --git a/src/adjoint/DASolver/DASimpleFoam/createRefsSimple.H b/src/adjoint/DASolver/DASimpleFoam/createRefsSimple.H
index cd6ddfd2..7e34ce83 100755
--- a/src/adjoint/DASolver/DASimpleFoam/createRefsSimple.H
+++ b/src/adjoint/DASolver/DASimpleFoam/createRefsSimple.H
@@ -15,6 +15,6 @@ volVectorField& fvSource = fvSourcePtr_();
 IOMRFZoneList& MRF = MRFPtr_();
 
 // create a file to store the objective values
-this->initializeObjFuncHistFilePtr("objFuncHist");
+this->initializeObjFuncHistFilePtr("objFuncTimeSeries");
 
 this->setDAObjFuncList();
diff --git a/src/adjoint/DASolver/DASimpleTFoam/createRefsSimpleT.H b/src/adjoint/DASolver/DASimpleTFoam/createRefsSimpleT.H
index c27c75c3..8653bb3f 100755
--- a/src/adjoint/DASolver/DASimpleTFoam/createRefsSimpleT.H
+++ b/src/adjoint/DASolver/DASimpleTFoam/createRefsSimpleT.H
@@ -17,6 +17,6 @@ dimensionedScalar Prt = PrtPtr_();
 volScalarField& alphat = alphatPtr_();
 
 // create a file to store the objective values
-this->initializeObjFuncHistFilePtr("objFuncHist");
+this->initializeObjFuncHistFilePtr("objFuncTimeSeries");
 
 this->setDAObjFuncList();
diff --git a/src/adjoint/DASolver/DASolidDisplacementFoam/createRefsSolidDisplacement.H b/src/adjoint/DASolver/DASolidDisplacementFoam/createRefsSolidDisplacement.H
index d5583e3d..17e425b9 100755
--- a/src/adjoint/DASolver/DASolidDisplacementFoam/createRefsSolidDisplacement.H
+++ b/src/adjoint/DASolver/DASolidDisplacementFoam/createRefsSolidDisplacement.H
@@ -11,6 +11,6 @@ volTensorField& gradD = gradDPtr_();
 volVectorField& divSigmaExp = divSigmaExpPtr_();
 
 // create a file to store the objective values
-this->initializeObjFuncHistFilePtr("objFuncHist");
+this->initializeObjFuncHistFilePtr("objFuncTimeSeries");
 
 this->setDAObjFuncList();
diff --git a/src/adjoint/DASolver/DASolver.C b/src/adjoint/DASolver/DASolver.C
index a64f4ac8..fcc5fa6d 100755
--- a/src/adjoint/DASolver/DASolver.C
+++ b/src/adjoint/DASolver/DASolver.C
@@ -431,6 +431,10 @@ void DASolver::calcPrimalResidualStatistics(
         // print the primal residuals to screen
         Info << "Printing Primal Residual Statistics." << endl;
     }
+    else if (mode == "calc")
+    {
+        // we will just calculate but not printting anything
+    }
     else
     {
         FatalErrorIn("") << "mode not valid" << abort(FatalError);
@@ -3074,6 +3078,7 @@ void DASolver::calcdFdXvAD(
             }
         }
         meshPtr_->movePoints(meshPoints);
+        meshPtr_->moving(false);
         // update all intermediate variables and boundary conditions
         daResidualPtr_->correctBoundaryConditions();
         daResidualPtr_->updateIntermediateVariables();
@@ -3179,6 +3184,7 @@ void DASolver::calcdRdXvTPsiAD(
         }
     }
     meshPtr_->movePoints(meshPoints);
+    meshPtr_->moving(false);
     // compute residuals
     daResidualPtr_->correctBoundaryConditions();
     daResidualPtr_->updateIntermediateVariables();
@@ -3577,25 +3583,127 @@ void DASolver::calcdRdActTPsiAD(
 #endif
 }
 
-void DASolver::registerStateVariableInput4AD()
+void DASolver::calcdRdWOldTPsiAD(
+    const label oldTimeLevel,
+    const Vec psi,
+    Vec dRdWOldTPsi)
+{
+#if defined(CODI_AD_FORWARD) || defined(CODI_AD_REVERSE)
+    /*
+    Description:
+        Compute the matrix-vector products dRdWOld^T*Psi using reverse-mode AD
+        Here WOld means the state variable from previous time step,
+        if oldTimeLevel = 1, WOld means W0, if oldTimeLevel=2, WOld means W00
+        R is always the residuals for the current time step
+        NOTE: if the oldTimeLevel is greater than the max nOldTimes a variable 
+        has, the derivative will be zero. This is done by registering input
+        only for variables that have enough oldTimes in registerStateVariableInput4AD
+    
+    Input:
+
+        oldTimeLevel: 1-dRdW0^T  2-dRdW00^T
+
+        psi: the vector to multiply dRdW0^T
+    
+    Output:
+        dRdWOldTPsi: the matrix-vector products dRdWOld^T * Psi
+    */
+
+    Info << "Calculating [dRdWOld]^T * Psi using reverse-mode AD with level " << oldTimeLevel << endl;
+
+    VecZeroEntries(dRdWOldTPsi);
+
+    this->globalADTape_.reset();
+    this->globalADTape_.setActive();
+
+    this->registerStateVariableInput4AD(oldTimeLevel);
+
+    // compute residuals
+    daResidualPtr_->correctBoundaryConditions();
+    daResidualPtr_->updateIntermediateVariables();
+    daModelPtr_->correctBoundaryConditions();
+    daModelPtr_->updateIntermediateVariables();
+    label isPC = 0;
+    dictionary options;
+    options.set("isPC", isPC);
+    daResidualPtr_->calcResiduals(options);
+    daModelPtr_->calcResiduals(options);
+
+    this->registerResidualOutput4AD();
+    this->globalADTape_.setPassive();
+
+    this->assignVec2ResidualGradient(psi);
+    this->globalADTape_.evaluate();
+
+    // get the deriv values
+    this->assignStateGradient2Vec(dRdWOldTPsi, oldTimeLevel);
+
+    // NOTE: we need to normalize dRdWOldTPsi!
+    this->normalizeGradientVec(dRdWOldTPsi);
+
+    VecAssemblyBegin(dRdWOldTPsi);
+    VecAssemblyEnd(dRdWOldTPsi);
+
+    this->globalADTape_.clearAdjoints();
+    this->globalADTape_.reset();
+
+    if (daOptionPtr_->getOption<label>("writeJacobians"))
+    {
+        word outputName = "dRdWOldTPsi";
+        DAUtility::writeVectorBinary(dRdWOldTPsi, outputName);
+        DAUtility::writeVectorASCII(dRdWOldTPsi, outputName);
+    }
+#endif
+}
+
+void DASolver::registerStateVariableInput4AD(const label oldTimeLevel)
 {
 #if defined(CODI_AD_FORWARD) || defined(CODI_AD_REVERSE)
     /*
     Description:
         Register all state variables as the input for reverse-mode AD
+    
+    Input:
+        oldTimeLevel: which time level to register, the default value
+        is 0, meaning it will register the state itself. If its 
+        value is 1, it will register state.oldTime(), if its value
+        is 2, it will register state.oldTime().oldTime(). For
+        steady-state adjoint oldTimeLevel = 0
     */
 
+    if (oldTimeLevel < 0 || oldTimeLevel > 2)
+    {
+        FatalErrorIn("") << "oldTimeLevel not valid. Options: 0, 1, or 2"
+                         << abort(FatalError);
+    }
+
     forAll(stateInfo_["volVectorStates"], idxI)
     {
         const word stateName = stateInfo_["volVectorStates"][idxI];
         volVectorField& state = const_cast<volVectorField&>(
             meshPtr_->thisDb().lookupObject<volVectorField>(stateName));
 
-        forAll(state, cellI)
+        label maxOldTimes = state.nOldTimes();
+
+        if (maxOldTimes >= oldTimeLevel)
         {
-            for (label i = 0; i < 3; i++)
+            forAll(state, cellI)
             {
-                this->globalADTape_.registerInput(state[cellI][i]);
+                for (label i = 0; i < 3; i++)
+                {
+                    if (oldTimeLevel == 0)
+                    {
+                        this->globalADTape_.registerInput(state[cellI][i]);
+                    }
+                    else if (oldTimeLevel == 1)
+                    {
+                        this->globalADTape_.registerInput(state.oldTime()[cellI][i]);
+                    }
+                    else if (oldTimeLevel == 2)
+                    {
+                        this->globalADTape_.registerInput(state.oldTime().oldTime()[cellI][i]);
+                    }
+                }
             }
         }
     }
@@ -3606,9 +3714,25 @@ void DASolver::registerStateVariableInput4AD()
         volScalarField& state = const_cast<volScalarField&>(
             meshPtr_->thisDb().lookupObject<volScalarField>(stateName));
 
-        forAll(state, cellI)
+        label maxOldTimes = state.nOldTimes();
+
+        if (maxOldTimes >= oldTimeLevel)
         {
-            this->globalADTape_.registerInput(state[cellI]);
+            forAll(state, cellI)
+            {
+                if (oldTimeLevel == 0)
+                {
+                    this->globalADTape_.registerInput(state[cellI]);
+                }
+                else if (oldTimeLevel == 1)
+                {
+                    this->globalADTape_.registerInput(state.oldTime()[cellI]);
+                }
+                else if (oldTimeLevel == 2)
+                {
+                    this->globalADTape_.registerInput(state.oldTime().oldTime()[cellI]);
+                }
+            }
         }
     }
 
@@ -3618,9 +3742,25 @@ void DASolver::registerStateVariableInput4AD()
         volScalarField& state = const_cast<volScalarField&>(
             meshPtr_->thisDb().lookupObject<volScalarField>(stateName));
 
-        forAll(state, cellI)
+        label maxOldTimes = state.nOldTimes();
+
+        if (maxOldTimes >= oldTimeLevel)
         {
-            this->globalADTape_.registerInput(state[cellI]);
+            forAll(state, cellI)
+            {
+                if (oldTimeLevel == 0)
+                {
+                    this->globalADTape_.registerInput(state[cellI]);
+                }
+                else if (oldTimeLevel == 1)
+                {
+                    this->globalADTape_.registerInput(state.oldTime()[cellI]);
+                }
+                else if (oldTimeLevel == 2)
+                {
+                    this->globalADTape_.registerInput(state.oldTime().oldTime()[cellI]);
+                }
+            }
         }
     }
 
@@ -3630,15 +3770,42 @@ void DASolver::registerStateVariableInput4AD()
         surfaceScalarField& state = const_cast<surfaceScalarField&>(
             meshPtr_->thisDb().lookupObject<surfaceScalarField>(stateName));
 
-        forAll(state, faceI)
-        {
-            this->globalADTape_.registerInput(state[faceI]);
-        }
-        forAll(state.boundaryField(), patchI)
+        label maxOldTimes = state.nOldTimes();
+
+        if (maxOldTimes >= oldTimeLevel)
         {
-            forAll(state.boundaryField()[patchI], faceI)
+            forAll(state, faceI)
+            {
+                if (oldTimeLevel == 0)
+                {
+                    this->globalADTape_.registerInput(state[faceI]);
+                }
+                else if (oldTimeLevel == 1)
+                {
+                    this->globalADTape_.registerInput(state.oldTime()[faceI]);
+                }
+                else if (oldTimeLevel == 2)
+                {
+                    this->globalADTape_.registerInput(state.oldTime().oldTime()[faceI]);
+                }
+            }
+            forAll(state.boundaryField(), patchI)
             {
-                this->globalADTape_.registerInput(state.boundaryFieldRef()[patchI][faceI]);
+                forAll(state.boundaryField()[patchI], faceI)
+                {
+                    if (oldTimeLevel == 0)
+                    {
+                        this->globalADTape_.registerInput(state.boundaryFieldRef()[patchI][faceI]);
+                    }
+                    else if (oldTimeLevel == 1)
+                    {
+                        this->globalADTape_.registerInput(state.oldTime().boundaryFieldRef()[patchI][faceI]);
+                    }
+                    else if (oldTimeLevel == 2)
+                    {
+                        this->globalADTape_.registerInput(state.oldTime().oldTime().boundaryFieldRef()[patchI][faceI]);
+                    }
+                }
             }
         }
     }
@@ -3944,7 +4111,9 @@ void DASolver::assignVec2ResidualGradient(Vec vecX)
 #endif
 }
 
-void DASolver::assignStateGradient2Vec(Vec vecY)
+void DASolver::assignStateGradient2Vec(
+    Vec vecY,
+    const label oldTimeLevel)
 {
 #if defined(CODI_AD_FORWARD) || defined(CODI_AD_REVERSE)
     /*
@@ -3953,12 +4122,24 @@ void DASolver::assignStateGradient2Vec(Vec vecY)
     
     Input:
         OpenFOAM state variables that contain the reverse-mode derivative 
+
+        oldTimeLevel: which time level to register, the default value
+        is 0, meaning it will register the state itself. If its 
+        value is 1, it will register state.oldTime(), if its value
+        is 2, it will register state.oldTime().oldTime(). For
+        steady-state adjoint oldTimeLevel = 0
     
     Output:
         vecY: a vector to store the derivatives. The order of this vector is 
         the same as the state variable vector
     */
 
+    if (oldTimeLevel < 0 || oldTimeLevel > 2)
+    {
+        FatalErrorIn("") << "oldTimeLevel not valid. Options: 0, 1, or 2"
+                         << abort(FatalError);
+    }
+
     PetscScalar* vecArray;
     VecGetArray(vecY, &vecArray);
 
@@ -3968,12 +4149,28 @@ void DASolver::assignStateGradient2Vec(Vec vecY)
         volVectorField& state = const_cast<volVectorField&>(
             meshPtr_->thisDb().lookupObject<volVectorField>(stateName));
 
-        forAll(meshPtr_->cells(), cellI)
+        label maxOldTimes = state.nOldTimes();
+
+        if (maxOldTimes >= oldTimeLevel)
         {
-            for (label i = 0; i < 3; i++)
+            forAll(meshPtr_->cells(), cellI)
             {
-                label localIdx = daIndexPtr_->getLocalAdjointStateIndex(stateName, cellI, i);
-                vecArray[localIdx] = state[cellI][i].getGradient();
+                for (label i = 0; i < 3; i++)
+                {
+                    label localIdx = daIndexPtr_->getLocalAdjointStateIndex(stateName, cellI, i);
+                    if (oldTimeLevel == 0)
+                    {
+                        vecArray[localIdx] = state[cellI][i].getGradient();
+                    }
+                    else if (oldTimeLevel == 1)
+                    {
+                        vecArray[localIdx] = state.oldTime()[cellI][i].getGradient();
+                    }
+                    else if (oldTimeLevel == 2)
+                    {
+                        vecArray[localIdx] = state.oldTime().oldTime()[cellI][i].getGradient();
+                    }
+                }
             }
         }
     }
@@ -3984,10 +4181,26 @@ void DASolver::assignStateGradient2Vec(Vec vecY)
         volScalarField& state = const_cast<volScalarField&>(
             meshPtr_->thisDb().lookupObject<volScalarField>(stateName));
 
-        forAll(meshPtr_->cells(), cellI)
+        label maxOldTimes = state.nOldTimes();
+
+        if (maxOldTimes >= oldTimeLevel)
         {
-            label localIdx = daIndexPtr_->getLocalAdjointStateIndex(stateName, cellI);
-            vecArray[localIdx] = state[cellI].getGradient();
+            forAll(meshPtr_->cells(), cellI)
+            {
+                label localIdx = daIndexPtr_->getLocalAdjointStateIndex(stateName, cellI);
+                if (oldTimeLevel == 0)
+                {
+                    vecArray[localIdx] = state[cellI].getGradient();
+                }
+                else if (oldTimeLevel == 1)
+                {
+                    vecArray[localIdx] = state.oldTime()[cellI].getGradient();
+                }
+                else if (oldTimeLevel == 2)
+                {
+                    vecArray[localIdx] = state.oldTime().oldTime()[cellI].getGradient();
+                }
+            }
         }
     }
 
@@ -3997,10 +4210,26 @@ void DASolver::assignStateGradient2Vec(Vec vecY)
         volScalarField& state = const_cast<volScalarField&>(
             meshPtr_->thisDb().lookupObject<volScalarField>(stateName));
 
-        forAll(meshPtr_->cells(), cellI)
+        label maxOldTimes = state.nOldTimes();
+
+        if (maxOldTimes >= oldTimeLevel)
         {
-            label localIdx = daIndexPtr_->getLocalAdjointStateIndex(stateName, cellI);
-            vecArray[localIdx] = state[cellI].getGradient();
+            forAll(meshPtr_->cells(), cellI)
+            {
+                label localIdx = daIndexPtr_->getLocalAdjointStateIndex(stateName, cellI);
+                if (oldTimeLevel == 0)
+                {
+                    vecArray[localIdx] = state[cellI].getGradient();
+                }
+                else if (oldTimeLevel == 1)
+                {
+                    vecArray[localIdx] = state.oldTime()[cellI].getGradient();
+                }
+                else if (oldTimeLevel == 2)
+                {
+                    vecArray[localIdx] = state.oldTime().oldTime()[cellI].getGradient();
+                }
+            }
         }
     }
 
@@ -4010,20 +4239,51 @@ void DASolver::assignStateGradient2Vec(Vec vecY)
         surfaceScalarField& state = const_cast<surfaceScalarField&>(
             meshPtr_->thisDb().lookupObject<surfaceScalarField>(stateName));
 
-        forAll(meshPtr_->faces(), faceI)
-        {
-            label localIdx = daIndexPtr_->getLocalAdjointStateIndex(stateName, faceI);
+        label maxOldTimes = state.nOldTimes();
 
-            if (faceI < daIndexPtr_->nLocalInternalFaces)
-            {
-                vecArray[localIdx] = state[faceI].getGradient();
-            }
-            else
+        if (maxOldTimes >= oldTimeLevel)
+        {
+            forAll(meshPtr_->faces(), faceI)
             {
-                label relIdx = faceI - daIndexPtr_->nLocalInternalFaces;
-                label patchIdx = daIndexPtr_->bFacePatchI[relIdx];
-                label faceIdx = daIndexPtr_->bFaceFaceI[relIdx];
-                vecArray[localIdx] = state.boundaryField()[patchIdx][faceIdx].getGradient();
+                label localIdx = daIndexPtr_->getLocalAdjointStateIndex(stateName, faceI);
+
+                if (faceI < daIndexPtr_->nLocalInternalFaces)
+                {
+                    if (oldTimeLevel == 0)
+                    {
+                        vecArray[localIdx] = state[faceI].getGradient();
+                    }
+                    else if (oldTimeLevel == 1)
+                    {
+                        vecArray[localIdx] = state.oldTime()[faceI].getGradient();
+                    }
+                    else if (oldTimeLevel == 2)
+                    {
+                        vecArray[localIdx] = state.oldTime().oldTime()[faceI].getGradient();
+                    }
+                }
+                else
+                {
+                    label relIdx = faceI - daIndexPtr_->nLocalInternalFaces;
+                    label patchIdx = daIndexPtr_->bFacePatchI[relIdx];
+                    label faceIdx = daIndexPtr_->bFaceFaceI[relIdx];
+
+                    if (oldTimeLevel == 0)
+                    {
+                        vecArray[localIdx] =
+                            state.boundaryField()[patchIdx][faceIdx].getGradient();
+                    }
+                    else if (oldTimeLevel == 1)
+                    {
+                        vecArray[localIdx] =
+                            state.oldTime().boundaryField()[patchIdx][faceIdx].getGradient();
+                    }
+                    else if (oldTimeLevel == 2)
+                    {
+                        vecArray[localIdx] =
+                            state.oldTime().oldTime().boundaryField()[patchIdx][faceIdx].getGradient();
+                    }
+                }
             }
         }
     }
@@ -4265,31 +4525,6 @@ void DASolver::writeObjFuncHistFile()
     return;
 }
 
-void DASolver::setTimeInstanceField(const label instanceI)
-{
-    /*
-    Description:
-        Assign primal variables based on the current time instance
-    */
-
-    FatalErrorIn("") << "setTimeInstanceField should be implemented in child classes!"
-                     << abort(FatalError);
-}
-
-scalar DASolver::getTimeInstanceObjFunc(
-    const label instanceI,
-    const word objFuncName)
-{
-    /*
-    Description:
-        Return the value of objective function at the given time instance and name
-    */
-    FatalErrorIn("") << "getTimeInstanceObjFunc should be implemented in child classes!"
-                     << abort(FatalError);
-
-    return 0.0;
-}
-
 label DASolver::isPrintTime(
     const Time& runTime,
     const label printInterval) const
@@ -4483,6 +4718,298 @@ void DASolver::updateBoundaryConditions(
     }
 }
 
+void DASolver::saveTimeInstanceFieldHybrid(label& timeInstanceI)
+{
+    /*
+    Description:
+        Save primal variable to time instance list for unsteady adjoint
+        Here we save the last nTimeInstances snapshots
+    */
+
+    scalar endTime = runTimePtr_->endTime().value();
+    scalar t = runTimePtr_->timeOutputValue();
+    scalar instanceStart =
+        endTime - periodicity_ / nTimeInstances_ * (nTimeInstances_ - 1 - timeInstanceI);
+
+    // the 2nd condition is for t=9.999999999999 scenario)
+    if (t > instanceStart || fabs(t - endTime) < 1e-8)
+    {
+        Info << "Saving time instance " << timeInstanceI << " at Time = " << t << endl;
+
+        // save fields
+        daFieldPtr_->ofField2List(
+            stateAllInstances_[timeInstanceI],
+            stateBoundaryAllInstances_[timeInstanceI]);
+
+        // save objective functions
+        forAll(daOptionPtr_->getAllOptions().subDict("objFunc").toc(), idxI)
+        {
+            word objFuncName = daOptionPtr_->getAllOptions().subDict("objFunc").toc()[idxI];
+            scalar objFuncVal = this->getObjFuncValue(objFuncName);
+            objFuncsAllInstances_[timeInstanceI].set(objFuncName, objFuncVal);
+        }
+
+        // save runTime
+        runTimeAllInstances_[timeInstanceI] = t;
+        runTimeIndexAllInstances_[timeInstanceI] = runTimePtr_->timeIndex();
+
+        if (daOptionPtr_->getOption<label>("debug"))
+        {
+            this->calcPrimalResidualStatistics("print");
+        }
+
+        timeInstanceI++;
+    }
+    return;
+}
+
+void DASolver::saveTimeInstanceFieldTimeAccurate(label& timeInstanceI)
+{
+    /*
+    Description:
+        Save primal variable to time instance list for unsteady adjoint
+        Here we save every time step
+    */
+    // save fields
+    daFieldPtr_->ofField2List(
+        stateAllInstances_[timeInstanceI],
+        stateBoundaryAllInstances_[timeInstanceI]);
+
+    // save objective functions
+    forAll(daOptionPtr_->getAllOptions().subDict("objFunc").toc(), idxI)
+    {
+        word objFuncName = daOptionPtr_->getAllOptions().subDict("objFunc").toc()[idxI];
+        scalar objFuncVal = this->getObjFuncValue(objFuncName);
+        objFuncsAllInstances_[timeInstanceI].set(objFuncName, objFuncVal);
+    }
+
+    // save runTime
+    scalar t = runTimePtr_->timeOutputValue();
+    runTimeAllInstances_[timeInstanceI] = t;
+    runTimeIndexAllInstances_[timeInstanceI] = runTimePtr_->timeIndex();
+
+    timeInstanceI++;
+}
+
+void DASolver::initOldTimes()
+{
+    /*
+    Description:
+        Initialize the oldTime for all state variables. We will create oldTime for
+        all state variables, no matter whether a variable actually need the oldTime()
+        field. This will allow setTimeInstanceField to correctly assign values for
+        oldTime(). NOTE: we need to call this function before calling setTimeInstanceField
+        Otherwise, the first setTimeInstanceField call will not get the correct
+        oldTime values.
+    */
+    forAll(stateInfo_["volVectorStates"], idxI)
+    {
+        const word stateName = stateInfo_["volVectorStates"][idxI];
+        volVectorField& state = const_cast<volVectorField&>(
+            meshPtr_->thisDb().lookupObject<volVectorField>(stateName));
+        // just create/initialize oldTimes
+        state.oldTime();
+        state.oldTime().oldTime();
+    }
+
+    forAll(stateInfo_["volScalarStates"], idxI)
+    {
+        const word stateName = stateInfo_["volScalarStates"][idxI];
+        volScalarField& state = const_cast<volScalarField&>(
+            meshPtr_->thisDb().lookupObject<volScalarField>(stateName));
+        // just create/initialize oldTimes
+        state.oldTime();
+        state.oldTime().oldTime();
+    }
+
+    forAll(stateInfo_["modelStates"], idxI)
+    {
+        const word stateName = stateInfo_["modelStates"][idxI];
+        volScalarField& state = const_cast<volScalarField&>(
+            meshPtr_->thisDb().lookupObject<volScalarField>(stateName));
+        // just create/initialize oldTimes
+        state.oldTime();
+        state.oldTime().oldTime();
+    }
+
+    forAll(stateInfo_["surfaceScalarStates"], idxI)
+    {
+        const word stateName = stateInfo_["surfaceScalarStates"][idxI];
+        surfaceScalarField& state = const_cast<surfaceScalarField&>(
+            meshPtr_->thisDb().lookupObject<surfaceScalarField>(stateName));
+        // just create/initialize oldTimes
+        state.oldTime();
+        state.oldTime().oldTime();
+    }
+}
+
+void DASolver::setTimeInstanceField(const label instanceI)
+{
+    /*
+    Description:
+        Assign primal variables based on the current time instance
+        If unsteady adjoint solvers are used, this virtual function should be 
+        implemented in a child class, otherwise, return error if called
+    */
+
+    Info << "Setting fields for time instance " << instanceI << endl;
+
+    label idxI = -9999;
+
+    // set run time
+    // NOTE: we need to call setTime before updating the oldTime fields, this is because
+    // the setTime call will assign field to field.oldTime()
+    runTimePtr_->setTime(runTimeAllInstances_[instanceI], runTimeIndexAllInstances_[instanceI]);
+
+    word mode = daOptionPtr_->getSubDictOption<word>("unsteadyAdjoint", "mode");
+
+    // set fields
+    label oldTimeLevel = 0;
+    daFieldPtr_->list2OFField(
+        stateAllInstances_[instanceI],
+        stateBoundaryAllInstances_[instanceI],
+        oldTimeLevel);
+
+    // for time accurate adjoint, in addition to assign current fields,
+    // we need to assign oldTime fields.
+    if (mode == "timeAccurateAdjoint")
+    {
+        // assign U.oldTime()
+        oldTimeLevel = 1;
+        // if instanceI - 1 < 0, we just assign idxI = 0. This is essentially
+        // assigning U.oldTime() = U0
+        idxI = max(instanceI - 1, 0);
+        daFieldPtr_->list2OFField(
+            stateAllInstances_[idxI],
+            stateBoundaryAllInstances_[idxI],
+            oldTimeLevel);
+
+        // assign U.oldTime().oldTime()
+        oldTimeLevel = 2;
+        // if instanceI - 2 < 0, we just assign idxI = 0, This is essentially
+        // assigning U.oldTime().oldTime() = U0
+        idxI = max(instanceI - 2, 0);
+        daFieldPtr_->list2OFField(
+            stateAllInstances_[idxI],
+            stateBoundaryAllInstances_[idxI],
+            oldTimeLevel);
+    }
+
+    // We need to call correctBC multiple times to reproduce
+    // the exact residual for mulitpoint, this is needed for some boundary conditions
+    // and intermediate variables (e.g., U for inletOutlet, nut with wall functions)
+    for (label i = 0; i < 10; i++)
+    {
+        daResidualPtr_->correctBoundaryConditions();
+        daResidualPtr_->updateIntermediateVariables();
+        daModelPtr_->correctBoundaryConditions();
+        daModelPtr_->updateIntermediateVariables();
+    }
+}
+
+void DASolver::setTimeInstanceVar(
+    const word mode,
+    Mat stateMat,
+    Mat stateBCMat,
+    Vec timeVec,
+    Vec timeIdxVec)
+{
+    PetscInt Istart, Iend;
+    MatGetOwnershipRange(stateMat, &Istart, &Iend);
+
+    PetscInt IstartBC, IendBC;
+    MatGetOwnershipRange(stateBCMat, &IstartBC, &IendBC);
+
+    for (label n = 0; n < nTimeInstances_; n++)
+    {
+        for (label i = Istart; i < Iend; i++)
+        {
+            label relIdx = i - Istart;
+            PetscScalar val;
+            if (mode == "mat2List")
+            {
+                MatGetValues(stateMat, 1, &i, 1, &n, &val);
+                stateAllInstances_[n][relIdx] = val;
+            }
+            else if (mode == "list2Mat")
+            {
+                assignValueCheckAD(val, stateAllInstances_[n][relIdx]);
+                MatSetValue(stateMat, i, n, val, INSERT_VALUES);
+            }
+            else
+            {
+                FatalErrorIn("") << "mode not valid!" << abort(FatalError);
+            }
+        }
+
+        for (label i = IstartBC; i < IendBC; i++)
+        {
+            label relIdx = i - IstartBC;
+            PetscScalar val;
+            if (mode == "mat2List")
+            {
+                MatGetValues(stateBCMat, 1, &i, 1, &n, &val);
+                stateBoundaryAllInstances_[n][relIdx] = val;
+            }
+            else if (mode == "list2Mat")
+            {
+                assignValueCheckAD(val, stateBoundaryAllInstances_[n][relIdx]);
+                MatSetValue(stateBCMat, i, n, val, INSERT_VALUES);
+            }
+            else
+            {
+                FatalErrorIn("") << "mode not valid!" << abort(FatalError);
+            }
+        }
+    }
+
+    if (mode == "list2Mat")
+    {
+        MatAssemblyBegin(stateMat, MAT_FINAL_ASSEMBLY);
+        MatAssemblyEnd(stateMat, MAT_FINAL_ASSEMBLY);
+        MatAssemblyBegin(stateBCMat, MAT_FINAL_ASSEMBLY);
+        MatAssemblyEnd(stateBCMat, MAT_FINAL_ASSEMBLY);
+    }
+
+    PetscScalar* timeVecArray;
+    PetscScalar* timeIdxVecArray;
+    VecGetArray(timeVec, &timeVecArray);
+    VecGetArray(timeIdxVec, &timeIdxVecArray);
+
+    for (label n = 0; n < nTimeInstances_; n++)
+    {
+        if (mode == "mat2List")
+        {
+            runTimeAllInstances_[n] = timeVecArray[n];
+            runTimeIndexAllInstances_[n] = round(timeIdxVecArray[n]);
+        }
+        else if (mode == "list2Mat")
+        {
+            assignValueCheckAD(timeVecArray[n], runTimeAllInstances_[n]);
+            timeIdxVecArray[n] = runTimeIndexAllInstances_[n];
+        }
+        else
+        {
+            FatalErrorIn("") << "mode not valid!" << abort(FatalError);
+        }
+    }
+
+    VecRestoreArray(timeVec, &timeVecArray);
+    VecRestoreArray(timeIdxVec, &timeIdxVecArray);
+}
+
+scalar DASolver::getTimeInstanceObjFunc(
+    const label instanceI,
+    const word objFuncName)
+{
+    /*
+    Description:
+        Return the value of objective function at the given time instance and name
+    */
+
+    return objFuncsAllInstances_[instanceI].getScalar(objFuncName);
+}
+
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
 } // End namespace Foam
diff --git a/src/adjoint/DASolver/DASolver.H b/src/adjoint/DASolver/DASolver.H
index 30615a94..4de0169b 100755
--- a/src/adjoint/DASolver/DASolver.H
+++ b/src/adjoint/DASolver/DASolver.H
@@ -170,6 +170,33 @@ protected:
     /// a flag in dRdWTMatVecMultFunction to determine if the global tap is initialized
     label globalADTape4dRdWTInitialized = 0;
 
+    /// state variable list for all instances (unsteady)
+    List<List<scalar>> stateAllInstances_;
+
+    /// state boundary variable list for all instances (unsteady)
+    List<List<scalar>> stateBoundaryAllInstances_;
+
+    /// objective function for all instances (unsteady)
+    List<dictionary> objFuncsAllInstances_;
+
+    /// the runtime value for all instances (unsteady)
+    List<scalar> runTimeAllInstances_;
+
+    /// the runtime index for all instances (unsteady)
+    List<label> runTimeIndexAllInstances_;
+
+    /// number of time instances for hybird adjoint (unsteady)
+    label nTimeInstances_ = -9999;
+
+    /// periodicity of oscillating flow variables (unsteady)
+    scalar periodicity_ = 0.0;
+
+    /// save primal variable to time instance list for hybrid adjoint (unsteady)
+    void saveTimeInstanceFieldHybrid(label& timeInstanceI);
+
+    /// save primal variable to time instance list for time accurate adjoint (unsteady)
+    void saveTimeInstanceFieldTimeAccurate(label& timeInstanceI);
+
 public:
     /// Runtime type information
     TypeName("DASolver");
@@ -214,13 +241,24 @@ public:
         Vec wVec) = 0;
 
     /// assign primal variables based on the current time instance
-    virtual void setTimeInstanceField(const label instanceI);
+    void setTimeInstanceField(const label instanceI);
 
     /// return the value of objective function at the given time instance and name
-    virtual scalar getTimeInstanceObjFunc(
+    scalar getTimeInstanceObjFunc(
         const label instanceI,
         const word objFuncName);
 
+    /// assign the time instance mats to/from the lists in the OpenFOAM layer depending on the mode
+    void setTimeInstanceVar(
+        const word mode,
+        Mat stateMat,
+        Mat stateBCMat,
+        Vec timeVec,
+        Vec timeIdxVec);
+    
+    /// initialize the oldTime for all state variables
+    void initOldTimes();
+
     /// compute dRdWT
     void calcdRdWT(
         const Vec xvVec,
@@ -410,6 +448,12 @@ public:
         const word designVarName,
         Vec dFdACT);
 
+    /// compute dRdWOld^T*Psi
+    void calcdRdWOldTPsiAD(
+        const label oldTimeLevel,
+        const Vec psi,
+        Vec dRdWOldTPsi);
+
     /// matrix free matrix-vector product function to compute vecY=dRdWT*vecX
     static PetscErrorCode dRdWTMatVecMultFunction(
         Mat dRdWT,
@@ -425,7 +469,7 @@ public:
     void destroydRdWTMatrixFree();
 
     /// register all state variables as the input for reverse-mode AD
-    void registerStateVariableInput4AD();
+    void registerStateVariableInput4AD(const label oldTimeLevel = 0);
 
     /// register field variables as the input for reverse-mode AD
     void registerFieldVariableInput4AD(
@@ -439,7 +483,9 @@ public:
     void assignVec2ResidualGradient(Vec vecX);
 
     /// set the reverse-mode AD derivatives from the state variables in OpenFOAM to vecY
-    void assignStateGradient2Vec(Vec vecY);
+    void assignStateGradient2Vec(
+        Vec vecY,
+        const label oldTimeLevel = 0);
 
     /// set the reverse-mode AD derivatives from the field variables in OpenFOAM to vecY
     void assignFieldGradient2Vec(
@@ -554,6 +600,12 @@ public:
         return daIndexPtr_->nLocalAdjointStates;
     }
 
+    /// return the number of local adjoint boundary states
+    label getNLocalAdjointBoundaryStates() const
+    {
+        return daIndexPtr_->nLocalAdjointBoundaryStates;
+    }
+
     /// return the number of local cells
     label getNLocalCells() const
     {
diff --git a/src/adjoint/DASolver/DATurboFoam/createRefsTurbo.H b/src/adjoint/DASolver/DATurboFoam/createRefsTurbo.H
index 421148be..9ff26605 100755
--- a/src/adjoint/DASolver/DATurboFoam/createRefsTurbo.H
+++ b/src/adjoint/DASolver/DATurboFoam/createRefsTurbo.H
@@ -17,6 +17,6 @@ const dictionary& allOptions = daOptionPtr_->getAllOptions();
 IOMRFZoneList& MRF = MRFPtr_();
 
 // create a file to store the objective values
-this->initializeObjFuncHistFilePtr("objFuncHist");
+this->initializeObjFuncHistFilePtr("objFuncTimeSeries");
 
 this->setDAObjFuncList();
diff --git a/src/adjoint/DAStateInfo/DAStateInfoLaplacianFoam.C b/src/adjoint/DAStateInfo/DAStateInfoLaplacianFoam.C
new file mode 100755
index 00000000..0e91990a
--- /dev/null
+++ b/src/adjoint/DAStateInfo/DAStateInfoLaplacianFoam.C
@@ -0,0 +1,81 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+\*---------------------------------------------------------------------------*/
+
+#include "DAStateInfoLaplacianFoam.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+defineTypeNameAndDebug(DAStateInfoLaplacianFoam, 0);
+addToRunTimeSelectionTable(DAStateInfo, DAStateInfoLaplacianFoam, dictionary);
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+DAStateInfoLaplacianFoam::DAStateInfoLaplacianFoam(
+    const word modelType,
+    const fvMesh& mesh,
+    const DAOption& daOption,
+    const DAModel& daModel)
+    : DAStateInfo(modelType, mesh, daOption, daModel)
+{
+    /*
+    Description:
+        Register the names of state variables
+        NOTE:
+        For model variables, such as turbulence model, register specific names
+        For example, register "nut" to modelStates for RANS turbulence models,
+        Then, we will call correctModelStates(stateInfo_["modelStates"]) to modify
+        "nut" based on the selected turbulence model. For example, for SA model,
+        correctModelStates will just replace "nut" with "nuTilda", for SST model,
+        it will replace "nut" with "k" and append "omega" to modelStates.
+        In other words, the model variables will be modified based on the selected
+        models at runtime.
+    */
+
+    stateInfo_["volScalarStates"].append("T");
+
+    /* 
+    Description:
+        Adjoint state connectivity info, numbers denote the level of connectivity
+        N/A means this state does not connect to the corrsponding residual 
+    
+                     D    
+        DRes         2   
+    
+        ******************************** NOTE 1 **********************************
+        One does not need to specify connectivity for each physical model, set the 
+        connectivity for original variables instead. For example, for turbulence models,
+        set nut. Then, how is nut connected to the other turbulence states will be 
+        set in the DAModel class. This is done by calling correctStateResidualModelCon. 
+        For example, for SA model we just replace nut with nuTilda, for SST model, we need 
+        to add extract connectivity since nut depends on grad(U), k, and omega. We need
+        to do this for other pyhsical models such as radiation models.
+        **************************************************************************
+    
+        ******************************** NOTE 2 **********************************
+        Do not specify physical model connectivity here, because they will be added
+        by calling addModelResidualCon. For example, for the SA turbulence
+        model, it will add the nuTildaRes to stateResConInfo_ and setup
+        its connectivity automatically.
+        **************************************************************************
+
+    */
+
+    stateResConInfo_.set(
+        "TRes",
+        {
+            {"T"}, // lv0
+            {"T"}, // lv1
+            {"T"} // lv2
+        });
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// ************************************************************************* //
diff --git a/src/adjoint/DAStateInfo/DAStateInfoLaplacianFoam.H b/src/adjoint/DAStateInfo/DAStateInfoLaplacianFoam.H
new file mode 100755
index 00000000..3cd78fb7
--- /dev/null
+++ b/src/adjoint/DAStateInfo/DAStateInfoLaplacianFoam.H
@@ -0,0 +1,55 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+    Description:
+        Child class for DALaplacianFoam
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef DAStateInfoLaplacianFoam_H
+#define DAStateInfoLaplacianFoam_H
+
+#include "DAStateInfo.H"
+#include "addToRunTimeSelectionTable.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+/*---------------------------------------------------------------------------*\
+      Class DAStateInfoLaplacianFoam Declaration
+\*---------------------------------------------------------------------------*/
+
+class DAStateInfoLaplacianFoam
+    : public DAStateInfo
+{
+
+public:
+    TypeName("DALaplacianFoam");
+    // Constructors
+
+    //- Construct from components
+    DAStateInfoLaplacianFoam(
+        const word modelType,
+        const fvMesh& mesh,
+        const DAOption& daOption,
+        const DAModel& daModel);
+
+    //- Destructor
+    virtual ~DAStateInfoLaplacianFoam()
+    {
+    }
+};
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //
diff --git a/src/adjoint/DAStateInfo/DAStateInfoPimpleFoam.C b/src/adjoint/DAStateInfo/DAStateInfoPimpleFoam.C
new file mode 100755
index 00000000..effbc2f8
--- /dev/null
+++ b/src/adjoint/DAStateInfo/DAStateInfoPimpleFoam.C
@@ -0,0 +1,116 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+\*---------------------------------------------------------------------------*/
+
+#include "DAStateInfoPimpleFoam.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+defineTypeNameAndDebug(DAStateInfoPimpleFoam, 0);
+addToRunTimeSelectionTable(DAStateInfo, DAStateInfoPimpleFoam, dictionary);
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+DAStateInfoPimpleFoam::DAStateInfoPimpleFoam(
+    const word modelType,
+    const fvMesh& mesh,
+    const DAOption& daOption,
+    const DAModel& daModel)
+    : DAStateInfo(modelType, mesh, daOption, daModel)
+{
+    /*
+    Description:
+        Register the names of state variables
+        NOTE:
+        For model variables, such as turbulence model, register specific names
+        For example, register "nut" to modelStates for RANS turbulence models,
+        Then, we will call correctModelStates(stateInfo_["modelStates"]) to modify
+        "nut" based on the selected turbulence model. For example, for SA model,
+        correctModelStates will just replace "nut" with "nuTilda", for SST model,
+        it will replace "nut" with "k" and append "omega" to modelStates.
+        In other words, the model variables will be modified based on the selected
+        models at runtime.
+    */
+
+    stateInfo_["volScalarStates"].append("p");
+    stateInfo_["modelStates"].append("nut");
+    stateInfo_["volVectorStates"].append("U");
+    stateInfo_["surfaceScalarStates"].append("phi");
+
+    // correct the names for model states based on the selected physical model at runtime
+    daModel.correctModelStates(stateInfo_["modelStates"]);
+
+    /* 
+    Description:
+        Adjoint state connectivity info, numbers denote the level of connectivity
+        N/A means this state does not connect to the corrsponding residual 
+    
+                     U      T      p     nut    phi
+        URes         2      2      1      1      0
+        TRes         2      2      2      1      0
+        pRes         3      2      2      2      1
+        phiRes       2      2      1      1      0
+    
+        ******************************** NOTE 1 **********************************
+        One does not need to specify connectivity for each physical model, set the 
+        connectivity for original variables instead. For example, for turbulence models,
+        set nut. Then, how is nut connected to the other turbulence states will be 
+        set in the DAModel class. This is done by calling correctStateResidualModelCon. 
+        For example, for SA model we just replace nut with nuTilda, for SST model, we need 
+        to add extract connectivity since nut depends on grad(U), k, and omega. We need
+        to do this for other pyhsical models such as radiation models.
+        **************************************************************************
+    
+        ******************************** NOTE 2 **********************************
+        Do not specify physical model connectivity here, because they will be added
+        by calling addModelResidualCon. For example, for the SA turbulence
+        model, it will add the nuTildaRes to stateResConInfo_ and setup
+        its connectivity automatically.
+        **************************************************************************
+
+    */
+
+    stateResConInfo_.set(
+        "URes",
+        {
+            {"U", "p", "nut", "phi"}, // lv0
+            {"U", "p", "nut"}, // lv1
+            {"U"} // lv2
+        });
+
+    stateResConInfo_.set(
+        "pRes",
+        {
+            {"U", "p", "nut", "phi"}, // lv0
+            {"U", "p", "nut", "phi"}, // lv1
+            {"U", "p", "nut"}, // lv2
+            {"U"} // lv3
+        });
+
+    stateResConInfo_.set(
+        "phiRes",
+        {
+            {"U", "p", "nut", "phi"}, // lv0
+            {"U", "p", "nut"}, // lv1
+            {"U"}, // lv2
+        });
+
+    // need to correct connectivity for physical models for each residual
+    daModel.correctStateResidualModelCon(stateResConInfo_["URes"]);
+    daModel.correctStateResidualModelCon(stateResConInfo_["pRes"]);
+    daModel.correctStateResidualModelCon(stateResConInfo_["phiRes"]);
+
+    // add physical model residual connectivity
+    daModel.addModelResidualCon(stateResConInfo_);
+
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// ************************************************************************* //
diff --git a/src/adjoint/DAStateInfo/DAStateInfoPimpleFoam.H b/src/adjoint/DAStateInfo/DAStateInfoPimpleFoam.H
new file mode 100755
index 00000000..8300bb8c
--- /dev/null
+++ b/src/adjoint/DAStateInfo/DAStateInfoPimpleFoam.H
@@ -0,0 +1,55 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+    Description:
+        Child class for DAPimpleFoam
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef DAStateInfoPimpleFoam_H
+#define DAStateInfoPimpleFoam_H
+
+#include "DAStateInfo.H"
+#include "addToRunTimeSelectionTable.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+/*---------------------------------------------------------------------------*\
+      Class DAStateInfoPimpleFoam Declaration
+\*---------------------------------------------------------------------------*/
+
+class DAStateInfoPimpleFoam
+    : public DAStateInfo
+{
+
+public:
+    TypeName("DAPimpleFoam");
+    // Constructors
+
+    //- Construct from components
+    DAStateInfoPimpleFoam(
+        const word modelType,
+        const fvMesh& mesh,
+        const DAOption& daOption,
+        const DAModel& daModel);
+
+    //- Destructor
+    virtual ~DAStateInfoPimpleFoam()
+    {
+    }
+};
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //
diff --git a/src/adjoint/DAStateInfo/DAStateInfoScalarTransportFoam.C b/src/adjoint/DAStateInfo/DAStateInfoScalarTransportFoam.C
new file mode 100755
index 00000000..0ccf3b77
--- /dev/null
+++ b/src/adjoint/DAStateInfo/DAStateInfoScalarTransportFoam.C
@@ -0,0 +1,81 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+\*---------------------------------------------------------------------------*/
+
+#include "DAStateInfoScalarTransportFoam.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+defineTypeNameAndDebug(DAStateInfoScalarTransportFoam, 0);
+addToRunTimeSelectionTable(DAStateInfo, DAStateInfoScalarTransportFoam, dictionary);
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+DAStateInfoScalarTransportFoam::DAStateInfoScalarTransportFoam(
+    const word modelType,
+    const fvMesh& mesh,
+    const DAOption& daOption,
+    const DAModel& daModel)
+    : DAStateInfo(modelType, mesh, daOption, daModel)
+{
+    /*
+    Description:
+        Register the names of state variables
+        NOTE:
+        For model variables, such as turbulence model, register specific names
+        For example, register "nut" to modelStates for RANS turbulence models,
+        Then, we will call correctModelStates(stateInfo_["modelStates"]) to modify
+        "nut" based on the selected turbulence model. For example, for SA model,
+        correctModelStates will just replace "nut" with "nuTilda", for SST model,
+        it will replace "nut" with "k" and append "omega" to modelStates.
+        In other words, the model variables will be modified based on the selected
+        models at runtime.
+    */
+
+    stateInfo_["volScalarStates"].append("T");
+
+    /* 
+    Description:
+        Adjoint state connectivity info, numbers denote the level of connectivity
+        N/A means this state does not connect to the corrsponding residual 
+    
+                     D    
+        DRes         2   
+    
+        ******************************** NOTE 1 **********************************
+        One does not need to specify connectivity for each physical model, set the 
+        connectivity for original variables instead. For example, for turbulence models,
+        set nut. Then, how is nut connected to the other turbulence states will be 
+        set in the DAModel class. This is done by calling correctStateResidualModelCon. 
+        For example, for SA model we just replace nut with nuTilda, for SST model, we need 
+        to add extract connectivity since nut depends on grad(U), k, and omega. We need
+        to do this for other pyhsical models such as radiation models.
+        **************************************************************************
+    
+        ******************************** NOTE 2 **********************************
+        Do not specify physical model connectivity here, because they will be added
+        by calling addModelResidualCon. For example, for the SA turbulence
+        model, it will add the nuTildaRes to stateResConInfo_ and setup
+        its connectivity automatically.
+        **************************************************************************
+
+    */
+
+    stateResConInfo_.set(
+        "TRes",
+        {
+            {"T"}, // lv0
+            {"T"}, // lv1
+            {"T"} // lv2
+        });
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// ************************************************************************* //
diff --git a/src/adjoint/DAStateInfo/DAStateInfoScalarTransportFoam.H b/src/adjoint/DAStateInfo/DAStateInfoScalarTransportFoam.H
new file mode 100755
index 00000000..daf8fc3e
--- /dev/null
+++ b/src/adjoint/DAStateInfo/DAStateInfoScalarTransportFoam.H
@@ -0,0 +1,55 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+    Description:
+        Child class for DAScalarTransportFoam
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef DAStateInfoScalarTransportFoam_H
+#define DAStateInfoScalarTransportFoam_H
+
+#include "DAStateInfo.H"
+#include "addToRunTimeSelectionTable.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+/*---------------------------------------------------------------------------*\
+      Class DAStateInfoScalarTransportFoam Declaration
+\*---------------------------------------------------------------------------*/
+
+class DAStateInfoScalarTransportFoam
+    : public DAStateInfo
+{
+
+public:
+    TypeName("DAScalarTransportFoam");
+    // Constructors
+
+    //- Construct from components
+    DAStateInfoScalarTransportFoam(
+        const word modelType,
+        const fvMesh& mesh,
+        const DAOption& daOption,
+        const DAModel& daModel);
+
+    //- Destructor
+    virtual ~DAStateInfoScalarTransportFoam()
+    {
+    }
+};
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //
diff --git a/src/adjoint/Make/files_Incompressible b/src/adjoint/Make/files_Incompressible
index e6c57a7d..119ac7fe 100755
--- a/src/adjoint/Make/files_Incompressible
+++ b/src/adjoint/Make/files_Incompressible
@@ -27,6 +27,7 @@ DAModel/DAModel.C
 DAStateInfo/DAStateInfo.C
 DAStateInfo/DAStateInfoSimpleFoam.C
 DAStateInfo/DAStateInfoPisoFoam.C
+DAStateInfo/DAStateInfoPimpleFoam.C
 DAStateInfo/DAStateInfoSimpleTFoam.C
 
 DAIndex/DAIndex.C
@@ -53,6 +54,7 @@ DAResidual/DAResidual.C
 DAResidual/DAResidualDummy.C
 DAResidual/DAResidualSimpleFoam.C
 DAResidual/DAResidualPisoFoam.C
+DAResidual/DAResidualPimpleFoam.C
 DAResidual/DAResidualSimpleTFoam.C
 
 DAColoring/DAColoring.C
@@ -80,8 +82,9 @@ DALinearEqn/DALinearEqn.C
 
 DASolver/DASolver.C
 DASolver/DASimpleFoam/DASimpleFoam.C
-DASolver/DAPisoFoam/DAPisoFoam.C
 DASolver/DASimpleTFoam/DASimpleTFoam.C
+DASolver/DAPisoFoam/DAPisoFoam.C
+DASolver/DAPimpleFoam/DAPimpleFoam.C
 
 boundaryConditions/multiFreqVector/multiFreqVectorFvPatchField.C
 boundaryConditions/nutUSpaldingWallFunctionDF/nutUSpaldingWallFunctionFvPatchScalarFieldDF.C
diff --git a/src/adjoint/Make/files_Solid b/src/adjoint/Make/files_Solid
index 69575f4a..fe00deac 100755
--- a/src/adjoint/Make/files_Solid
+++ b/src/adjoint/Make/files_Solid
@@ -10,20 +10,27 @@ DAModel/DAModel.C
 
 DAStateInfo/DAStateInfo.C
 DAStateInfo/DAStateInfoSolidDisplacementFoam.C
+DAStateInfo/DAStateInfoLaplacianFoam.C
+DAStateInfo/DAStateInfoScalarTransportFoam.C
 
 DAIndex/DAIndex.C
 
 DAField/DAField.C
 
+DAIntmdVar/DAIntmdVar.C
+
 DAObjFunc/DAObjFunc.C
 DAObjFunc/DAObjFuncVonMisesStressKS.C
 DAObjFunc/DAObjFuncMass.C
+DAObjFunc/DAObjFuncVariableVolSum.C
 
 DAFvSource/DAFvSource.C
 
 DAResidual/DAResidual.C
 DAResidual/DAResidualDummy.C
 DAResidual/DAResidualSolidDisplacementFoam.C
+DAResidual/DAResidualLaplacianFoam.C
+DAResidual/DAResidualScalarTransportFoam.C
 
 DAColoring/DAColoring.C
 
@@ -44,6 +51,8 @@ DALinearEqn/DALinearEqn.C
 
 DASolver/DASolver.C
 DASolver/DASolidDisplacementFoam/DASolidDisplacementFoam.C
+DASolver/DALaplacianFoam/DALaplacianFoam.C
+DASolver/DAScalarTransportFoam/DAScalarTransportFoam.C
 
 boundaryConditions/tractionDisplacement/tractionDisplacementFvPatchVectorField.C
 
diff --git a/src/include/DAMacroFunctions.H b/src/include/DAMacroFunctions.H
index 4f1e1965..02f4a03e 100755
--- a/src/include/DAMacroFunctions.H
+++ b/src/include/DAMacroFunctions.H
@@ -25,13 +25,6 @@
         const_cast<fieldType&>(                  \
             db.lookupObject<fieldType>(stateResName)));
 
-#define makeStatePartDeriv(regState, fieldType, db)          \
-    const word stateName = regState;                         \
-    const word statePartDerivName = stateName + "PartDeriv"; \
-    fieldType& statePartDeriv(                               \
-        const_cast<fieldType&>(                              \
-            db.lookupObject<fieldType>(statePartDerivName)));
-
 #define normalizeResiduals(resName)                                                                \
     if (!DAUtility::isInList<word>(#resName, daOption_.getOption<wordList>("normalizeResiduals"))) \
     {                                                                                              \
@@ -70,15 +63,7 @@
                 IOobject::NO_WRITE),                                  \
             mesh,                                                     \
             dimensionedScalar(#stateName "Res", stateUnit, 0.0),      \
-            zeroGradientFvPatchField<scalar>::typeName),                \
-        stateName##ResPartDeriv_(                                     \
-            IOobject(                                                 \
-                #stateName "ResPartDeriv",                            \
-                mesh.time().timeName(),                               \
-                mesh,                                                 \
-                IOobject::NO_READ,                                    \
-                IOobject::NO_WRITE),                                  \
-            stateName##Res_)
+            zeroGradientFvPatchField<scalar>::typeName)
 
 #define setResidualClassMemberVector(stateName, stateUnit)                \
     stateName##_(                                                         \
@@ -93,15 +78,7 @@
                 IOobject::NO_WRITE),                                      \
             mesh,                                                         \
             dimensionedVector(#stateName "Res", stateUnit, vector::zero), \
-            zeroGradientFvPatchField<vector>::typeName),                    \
-        stateName##ResPartDeriv_(                                         \
-            IOobject(                                                     \
-                #stateName "ResPartDeriv",                                \
-                mesh.time().timeName(),                                   \
-                mesh,                                                     \
-                IOobject::NO_READ,                                        \
-                IOobject::NO_WRITE),                                      \
-            stateName##Res_)
+            zeroGradientFvPatchField<vector>::typeName)
 
 #define setResidualClassMemberPhi(stateName)                              \
     stateName##_(                                                         \
@@ -114,14 +91,6 @@
                 mesh,                                                     \
                 IOobject::NO_READ,                                        \
                 IOobject::NO_WRITE),                                      \
-            mesh.thisDb().lookupObject<surfaceScalarField>(#stateName)),  \
-        stateName##ResPartDeriv_(                                         \
-            IOobject(                                                     \
-                #stateName "ResPartDeriv",                                \
-                mesh.time().timeName(),                                   \
-                mesh,                                                     \
-                IOobject::NO_READ,                                        \
-                IOobject::NO_WRITE),                                      \
             mesh.thisDb().lookupObject<surfaceScalarField>(#stateName))
 
 #endif
diff --git a/src/include/createPimpleControlPython.H b/src/include/createPimpleControlPython.H
new file mode 100755
index 00000000..a6ee836b
--- /dev/null
+++ b/src/include/createPimpleControlPython.H
@@ -0,0 +1,14 @@
+/*---------------------------------------------------------------------------*\
+
+    DAFoam  : Discrete Adjoint with OpenFOAM
+    Version : v2
+
+\*---------------------------------------------------------------------------*/
+
+Info << "Create pimpleControl." << endl;
+
+pimplePtr_.reset(
+    new pimpleControl(
+        mesh));
+
+pimpleControl& pimple = pimplePtr_();
diff --git a/src/pyDASolvers/DASolvers.H b/src/pyDASolvers/DASolvers.H
index 5fbb0962..1d3981b4 100755
--- a/src/pyDASolvers/DASolvers.H
+++ b/src/pyDASolvers/DASolvers.H
@@ -341,6 +341,15 @@ public:
         DASolverPtr_->calcdFdFieldAD(xvVec, wVec, objFuncName, designVarName, dFdField);
     }
 
+    /// compute dRdWOld^T*Psi
+    void calcdRdWOldTPsiAD(
+        const label oldTimeLevel,
+        const Vec psi,
+        Vec dRdWOldTPsi)
+    {
+        DASolverPtr_->calcdRdWOldTPsiAD(oldTimeLevel, psi, dRdWOldTPsi);
+    }
+
     /// Update the OpenFOAM field values (including both internal and boundary fields) based on the state vector wVec
     void updateOFField(const Vec wVec)
     {
@@ -385,6 +394,12 @@ public:
         return DASolverPtr_->getNLocalAdjointStates();
     }
 
+    /// return the number of local adjoint boundary states
+    label getNLocalAdjointBoundaryStates() const
+    {
+        return DASolverPtr_->getNLocalAdjointBoundaryStates();
+    }
+
     /// return the number of local cells
     label getNLocalCells() const
     {
@@ -509,6 +524,23 @@ public:
         DASolverPtr_->setTimeInstanceField(instanceI);
     }
 
+    /// initialize the oldTime for all state variables
+    void initOldTimes()
+    {
+        DASolverPtr_->initOldTimes();
+    }
+
+    /// assign the time instance mats to/from the lists in the OpenFOAM layer depending on the mode
+    void setTimeInstanceVar(
+        const word mode,
+        Mat stateMat,
+        Mat stateBCMat,
+        Vec timeVec,
+        Vec timeIdxVec)
+    {
+        DASolverPtr_->setTimeInstanceVar(mode, stateMat, stateBCMat, timeVec, timeIdxVec);
+    }
+
     /// return the value of objective function at the given time instance and name
     double getTimeInstanceObjFunc(
         const label instanceI,
@@ -536,6 +568,12 @@ public:
     {
         DASolverPtr_->updateBoundaryConditions(fieldName, fieldType);
     }
+
+    /// Calculate the mean, max, and norm2 for all residuals and print it to screen
+    void calcPrimalResidualStatistics(const word mode)
+    {
+        DASolverPtr_->calcPrimalResidualStatistics(mode, 0);
+    }
 };
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
diff --git a/src/pyDASolvers/pyDASolvers.pyx b/src/pyDASolvers/pyDASolvers.pyx
index c5552433..67ed2b1c 100755
--- a/src/pyDASolvers/pyDASolvers.pyx
+++ b/src/pyDASolvers/pyDASolvers.pyx
@@ -47,6 +47,7 @@ cdef extern from "DASolvers.H" namespace "Foam":
         void calcdRdACT(PetscVec, PetscVec, char *, char *, PetscMat)
         void calcdRdFieldTPsiAD(PetscVec, PetscVec, PetscVec, char *, PetscVec)
         void calcdFdFieldAD(PetscVec, PetscVec, char *, char *, PetscVec)
+        void calcdRdWOldTPsiAD(int, PetscVec, PetscVec)
         void convertMPIVec2SeqVec(PetscVec, PetscVec)
         void syncDAOptionToActuatorDVs()
         void updateOFField(PetscVec)
@@ -56,6 +57,7 @@ cdef extern from "DASolvers.H" namespace "Foam":
         void ofField2StateVec(PetscVec)
         void stateVec2OFField(PetscVec)
         int getNLocalAdjointStates()
+        int getNLocalAdjointBoundaryStates()
         int getNLocalCells()
         int checkMesh()
         double getObjFuncValue(char *)
@@ -74,9 +76,12 @@ cdef extern from "DASolvers.H" namespace "Foam":
         void readVectorBinary(PetscVec, char *)
         void writeVectorBinary(PetscVec, char *)
         void setTimeInstanceField(int)
+        void initOldTimes()
+        void setTimeInstanceVar(char *, PetscMat, PetscMat, PetscVec, PetscVec)
         double getTimeInstanceObjFunc(int, char *)
         void setFieldValue4GlobalCellI(char *, double, int, int)
         void updateBoundaryConditions(char *, char *)
+        void calcPrimalResidualStatistics(char *)
     
 # create python wrappers that call cpp functions
 cdef class pyDASolvers:
@@ -200,6 +205,9 @@ cdef class pyDASolvers:
 
     def calcdFdFieldAD(self, Vec xvVec, Vec wVec, objFuncName, designVarName, Vec dFdField):
         self._thisptr.calcdFdFieldAD(xvVec.vec, wVec.vec, objFuncName, designVarName, dFdField.vec)
+    
+    def calcdRdWOldTPsiAD(self, oldTimeLevel, Vec psi, Vec dRdWOldTPsi):
+        self._thisptr.calcdRdWOldTPsiAD(oldTimeLevel, psi.vec, dRdWOldTPsi.vec)
 
     def convertMPIVec2SeqVec(self, Vec mpiVec, Vec seqVec):
         self._thisptr.convertMPIVec2SeqVec(mpiVec.vec, seqVec.vec)
@@ -240,6 +248,9 @@ cdef class pyDASolvers:
     def getNLocalAdjointStates(self):
         return self._thisptr.getNLocalAdjointStates()
     
+    def getNLocalAdjointBoundaryStates(self):
+        return self._thisptr.getNLocalAdjointBoundaryStates()
+    
     def getNLocalCells(self):
         return self._thisptr.getNLocalCells()
     
@@ -279,6 +290,12 @@ cdef class pyDASolvers:
     def setTimeInstanceField(self, instanceI):
         self._thisptr.setTimeInstanceField(instanceI)
     
+    def initOldTimes(self):
+        self._thisptr.initOldTimes()
+    
+    def setTimeInstanceVar(self, mode, Mat stateMat, Mat stateBCMat, Vec timeVec, Vec timeIdxVec):
+        self._thisptr.setTimeInstanceVar(mode, stateMat.mat, stateBCMat.mat, timeVec.vec, timeIdxVec.vec)
+    
     def getTimeInstanceObjFunc(self, instanceI, objFuncName):
         return self._thisptr.getTimeInstanceObjFunc(instanceI, objFuncName)
 
@@ -287,3 +304,6 @@ cdef class pyDASolvers:
     
     def updateBoundaryConditions(self, fieldName, fieldType):
         self._thisptr.updateBoundaryConditions(fieldName, fieldType)
+    
+    def calcPrimalResidualStatistics(self, mode):
+        self._thisptr.calcPrimalResidualStatistics(mode)
diff --git a/tests/refs/DAFoam_Test_DAPisoFoamACTLRef.txt b/tests/refs/DAFoam_Test_DAPisoFoamACTLRef.txt
index c816c8d4..90c1bd08 100755
--- a/tests/refs/DAFoam_Test_DAPisoFoamACTLRef.txt
+++ b/tests/refs/DAFoam_Test_DAPisoFoamACTLRef.txt
@@ -1,44 +1,44 @@
 Dictionary Key: CD
-@value    2.580311771671191 1e-08 1e-10
+@value    2.711410261032643 1e-08 1e-10
 Dictionary Key: CL
-@value    15.38715312670266 1e-08 1e-10
+@value    15.03566583296491 1e-08 1e-10
 Dictionary Key: fail
 @value                    0 1e-08 1e-10
 Dictionary Key: CD
 Dictionary Key: actuator
-@value -0.06691540636835763 1e-06 1e-08
-@value   0.2031093084821273 1e-06 1e-08
-@value   0.4157274147557912 1e-06 1e-08
-@value   0.4173839168778466 1e-06 1e-08
-@value  -0.2730768254155285 1e-06 1e-08
-@value   0.1714905531909766 1e-06 1e-08
-@value  0.04129472872252628 1e-06 1e-08
-@value -0.005084590731402956 1e-06 1e-08
-@value -0.002852629255837884 1e-06 1e-08
-@value   0.1531743868700099 1e-06 1e-08
-@value   0.2031972720431217 1e-06 1e-08
+@value -0.01257117034324886 1e-05 1e-07
+@value   0.1865215310517349 1e-05 1e-07
+@value   0.4990474777474588 1e-05 1e-07
+@value   0.3909514211647941 1e-05 1e-07
+@value  -0.2538164293655455 1e-05 1e-07
+@value   0.1737145157741071 1e-05 1e-07
+@value  0.04257515179893158 1e-05 1e-07
+@value -0.004970176053270661 1e-05 1e-07
+@value 0.001413600397138935 1e-05 1e-07
+@value   0.1493711876702419 1e-05 1e-07
+@value   0.1989813108358617 1e-05 1e-07
 Dictionary Key: shapey
-@value    3.877925732103091 1e-06 1e-08
-@value    3.919124320073595 1e-06 1e-08
-@value    2.515227606321087 1e-06 1e-08
-@value    2.197580984478826 1e-06 1e-08
+@value    3.042351842126886 1e-05 1e-07
+@value     3.45992477814552 1e-05 1e-07
+@value    3.300088851348871 1e-05 1e-07
+@value    2.714811029889377 1e-05 1e-07
 Dictionary Key: CL
 Dictionary Key: actuator
-@value    4.625579555409113 1e-06 1e-08
-@value   -1.506256327117449 1e-06 1e-08
-@value   -1.665464586733235 1e-06 1e-08
-@value   -1.866416776730894 1e-06 1e-08
-@value    2.235023406885797 1e-06 1e-08
-@value  -0.4832923364612146 1e-06 1e-08
-@value  -0.1146694249132433 1e-06 1e-08
-@value  0.02252923805403577 1e-06 1e-08
-@value 0.0001834543906943214 1e-06 1e-08
-@value  -0.7017365674834073 1e-06 1e-08
-@value  -0.8773053580859722 1e-06 1e-08
+@value    3.224859580251757 1e-05 1e-07
+@value   -1.398642403438058 1e-05 1e-07
+@value   -3.223907450448617 1e-05 1e-07
+@value   -1.568663881376231 1e-05 1e-07
+@value    2.013655723823548 1e-05 1e-07
+@value  -0.5431107506425367 1e-05 1e-07
+@value  -0.1348825940832598 1e-05 1e-07
+@value  0.02136740316017564 1e-05 1e-07
+@value -0.04444474259903856 1e-05 1e-07
+@value  -0.6648861465579151 1e-05 1e-07
+@value  -0.8327244406091239 1e-05 1e-07
 Dictionary Key: shapey
-@value   -12.83734742872358 1e-06 1e-08
-@value   -3.750199461068074 1e-06 1e-08
-@value    32.86051644014564 1e-06 1e-08
-@value    22.78504907852622 1e-06 1e-08
+@value    2.891668577612543 1e-05 1e-07
+@value    12.06447092747541 1e-05 1e-07
+@value    18.08003309903899 1e-05 1e-07
+@value    7.302947463289298 1e-05 1e-07
 Dictionary Key: fail
-@value                    0 1e-06 1e-08
+@value                    0 1e-05 1e-07
\ No newline at end of file
diff --git a/tests/refs/DAFoam_Test_DAPisoFoamRef.txt b/tests/refs/DAFoam_Test_DAPisoFoamRef.txt
index 68370d7b..61b1742a 100755
--- a/tests/refs/DAFoam_Test_DAPisoFoamRef.txt
+++ b/tests/refs/DAFoam_Test_DAPisoFoamRef.txt
@@ -1,40 +1,40 @@
 Dictionary Key: CD
-@value -0.03930979518927642 1e-08 1e-10
+@value -0.04054742330022887 1e-08 1e-10
 Dictionary Key: CL
-@value    1.135472486770393 1e-08 1e-10
+@value    1.086700966831326 1e-08 1e-10
 Dictionary Key: fail
 @value                    0 1e-08 1e-10
 Dictionary Key: CD
 Dictionary Key: actuator
-@value  0.06036451758372193 1e-06 1e-08
-@value  0.08768044751282805 1e-06 1e-08
-@value   0.1349840600841809 1e-06 1e-08
-@value -0.07848751476214282 1e-06 1e-08
-@value  0.04006002121427141 1e-06 1e-08
-@value -0.02315571284032349 1e-06 1e-08
-@value    15.65603081841504 1e-06 1e-08
-@value  -0.0751110111304472 1e-06 1e-08
-@value -0.009728086161867011 1e-06 1e-08
+@value  0.03170355962739631 1e-05 1e-07
+@value    0.131824183114176 1e-05 1e-07
+@value     0.13674111070256 1e-05 1e-07
+@value -0.05534708469898308 1e-05 1e-07
+@value  0.02202459950829003 1e-05 1e-07
+@value -0.02633701150456399 1e-05 1e-07
+@value    14.68323169781665 1e-05 1e-07
+@value -0.07019523942503399 1e-05 1e-07
+@value -0.009386129913480812 1e-05 1e-07
 Dictionary Key: shapey
-@value   0.1095544933336656 1e-06 1e-08
-@value -0.009931564024135038 1e-06 1e-08
-@value -0.006349638175747467 1e-06 1e-08
-@value    0.052634109430707 1e-06 1e-08
+@value   0.1115554067088204 1e-05 1e-07
+@value  0.01769257286996475 1e-05 1e-07
+@value  -0.0159133728788409 1e-05 1e-07
+@value  0.02882756157455849 1e-05 1e-07
 Dictionary Key: CL
 Dictionary Key: actuator
-@value    1.354695537167285 1e-06 1e-08
-@value   -1.582780673916231 1e-06 1e-08
-@value  -0.5656799380560877 1e-06 1e-08
-@value   -0.392046229010535 1e-06 1e-08
-@value    1.176968172070254 1e-06 1e-08
-@value   0.1447782208050797 1e-06 1e-08
-@value   -20.31955157273847 1e-06 1e-08
-@value  0.08378143303377775 1e-06 1e-08
-@value  0.02440346060175714 1e-06 1e-08
+@value    1.301198513338533 1e-05 1e-07
+@value   -1.680357537381187 1e-05 1e-07
+@value  -0.4737249707408401 1e-05 1e-07
+@value  -0.3324203449768449 1e-05 1e-07
+@value    1.159269060573486 1e-05 1e-07
+@value   0.1181348719183022 1e-05 1e-07
+@value   -17.89222926911277 1e-05 1e-07
+@value  0.07402761836782278 1e-05 1e-07
+@value  0.02381631839551503 1e-05 1e-07
 Dictionary Key: shapey
-@value   0.2049215215694911 1e-06 1e-08
-@value   0.5784880606035294 1e-06 1e-08
-@value   0.6540246472118448 1e-06 1e-08
-@value    0.183560056605966 1e-06 1e-08
+@value   0.1865834491663586 1e-05 1e-07
+@value   0.5986393655280162 1e-05 1e-07
+@value   0.6870391331087209 1e-05 1e-07
+@value   0.1908608538816518 1e-05 1e-07
 Dictionary Key: fail
-@value                    0 1e-06 1e-08
+@value                    0 1e-05 1e-07
\ No newline at end of file
diff --git a/tests/refs/DAFoam_Test_DARhoSimpleCFoamADRef.txt b/tests/refs/DAFoam_Test_DARhoSimpleCFoamADRef.txt
index d995fabe..d60829fe 100755
--- a/tests/refs/DAFoam_Test_DARhoSimpleCFoamADRef.txt
+++ b/tests/refs/DAFoam_Test_DARhoSimpleCFoamADRef.txt
@@ -6,17 +6,17 @@ Dictionary Key: fail
 @value                    0 1e-08 1e-10
 Dictionary Key: CD
 Dictionary Key: alpha
-@value 0.004409101138894869 1e-06 1e-08
+@value 0.004409101138894869 1e-05 1e-07
 Dictionary Key: shapey
-@value -0.007122688413025238 1e-06 1e-08
-@value -0.02840771135269596 1e-06 1e-08
-@value  0.05265037400867181 1e-06 1e-08
+@value -0.007122688413025238 1e-05 1e-07
+@value -0.02840771135269596 1e-05 1e-07
+@value  0.05265037400867181 1e-05 1e-07
 Dictionary Key: CL
 Dictionary Key: alpha
-@value    0.172119723539071 1e-06 1e-08
+@value    0.172119723539071 1e-05 1e-07
 Dictionary Key: shapey
-@value    1.768909810680021 1e-06 1e-08
-@value    1.298866728663029 1e-06 1e-08
-@value     2.99871565148093 1e-06 1e-08
+@value    1.768909810680021 1e-05 1e-07
+@value    1.298866728663029 1e-05 1e-07
+@value     2.99871565148093 1e-05 1e-07
 Dictionary Key: fail
-@value                    0 1e-06 1e-08
\ No newline at end of file
+@value                    0 1e-05 1e-07
\ No newline at end of file
diff --git a/tests/refs/DAFoam_Test_DARhoSimpleCFoamRef.txt b/tests/refs/DAFoam_Test_DARhoSimpleCFoamRef.txt
index ab426531..cbd01f09 100755
--- a/tests/refs/DAFoam_Test_DARhoSimpleCFoamRef.txt
+++ b/tests/refs/DAFoam_Test_DARhoSimpleCFoamRef.txt
@@ -6,17 +6,17 @@ Dictionary Key: fail
 @value                    0 1e-08 1e-10
 Dictionary Key: CD
 Dictionary Key: alpha
-@value 0.004369406262371265 1e-06 1e-08
+@value 0.004369406262371265 1e-05 1e-07
 Dictionary Key: shapey
-@value  0.02695489140649832 1e-06 1e-08
-@value  0.05129793824684431 1e-06 1e-08
-@value   0.1311182482318767 1e-06 1e-08
+@value  0.02695489140649832 1e-05 1e-07
+@value  0.05129793824684431 1e-05 1e-07
+@value   0.1311182482318767 1e-05 1e-07
 Dictionary Key: CL
 Dictionary Key: alpha
-@value   0.1555238268597652 1e-06 1e-08
+@value   0.1555238268597652 1e-05 1e-07
 Dictionary Key: shapey
-@value    3.617957458008334 1e-06 1e-08
-@value    2.486507647606889 1e-06 1e-08
-@value    2.991696507735573 1e-06 1e-08
+@value    3.617957458008334 1e-05 1e-07
+@value    2.486507647606889 1e-05 1e-07
+@value    2.991696507735573 1e-05 1e-07
 Dictionary Key: fail
-@value                    0 1e-06 1e-08
+@value                    0 1e-05 1e-07
diff --git a/tests/refs/DAFoam_Test_DARhoSimpleFoamADRef.txt b/tests/refs/DAFoam_Test_DARhoSimpleFoamADRef.txt
index 73adb777..4f49312a 100755
--- a/tests/refs/DAFoam_Test_DARhoSimpleFoamADRef.txt
+++ b/tests/refs/DAFoam_Test_DARhoSimpleFoamADRef.txt
@@ -1,104 +1,104 @@
 Dictionary Key: CD
-@value  0.09346922813884119 1e-08 1e-10
+@value  0.09340147733565053 1e-08 1e-10
 Dictionary Key: CL
-@value   0.3122128251545178 1e-08 1e-10
+@value   0.3122281763132833 1e-08 1e-10
 Dictionary Key: CMZ
-@value   0.1623698698921813 1e-08 1e-10
+@value   0.1623386826890191 1e-08 1e-10
 Dictionary Key: VOL
-@value     97144.3677437709 1e-08 1e-10
+@value    97143.96412840074 1e-08 1e-10
 Dictionary Key: VOL1
-@value   0.4484304955304088 1e-08 1e-10
+@value                  1.2 1e-08 1e-10
 Dictionary Key: fail
 @value                    0 1e-08 1e-10
 Dictionary Key: CD
 Dictionary Key: actuator
-@value 7.073103635527384e-06 1e-06 1e-08
-@value -1.940351211080423e-05 1e-06 1e-08
-@value 3.16595332922842e-06 1e-06 1e-08
-@value 1.588142690285651e-05 1e-06 1e-08
-@value -1.991275163521597e-05 1e-06 1e-08
-@value -4.044842767517565e-06 1e-06 1e-08
-@value -8.470052833794986e-08 1e-06 1e-08
-@value 2.541873157003857e-05 1e-06 1e-08
-@value 3.877678298299797e-05 1e-06 1e-08
+@value 1.787880776776719e-05 1e-05 1e-07
+@value -5.988289890025471e-06 1e-05 1e-07
+@value -3.387760482016437e-06 1e-05 1e-07
+@value 8.798652802348822e-06 1e-05 1e-07
+@value 3.208206058617116e-05 1e-05 1e-07
+@value                    0 1e-05 1e-07
+@value -1.783836082388835e-07 1e-05 1e-07
+@value 4.782417148405217e-06 1e-05 1e-07
+@value -5.684522912625625e-06 1e-05 1e-07
 Dictionary Key: shapey
-@value   0.2205704966590456 1e-06 1e-08
-@value   0.1824021892163132 1e-06 1e-08
-@value    2.376200566749128 1e-06 1e-08
-@value    1.886264492371179 1e-06 1e-08
+@value   0.2204507679586138 1e-05 1e-07
+@value     0.18230436993821 1e-05 1e-07
+@value    2.376145960018849 1e-05 1e-07
+@value    1.886220050842116 1e-05 1e-07
 Dictionary Key: uin
-@value 0.003825074285916163 1e-06 1e-08
+@value  0.00382495280960852 1e-05 1e-07
 Dictionary Key: CL
 Dictionary Key: actuator
-@value -2.287999951136713e-05 1e-06 1e-08
-@value -0.0001064610773344815 1e-06 1e-08
-@value -3.393741587479372e-06 1e-06 1e-08
-@value -1.153126087328061e-05 1e-06 1e-08
-@value -3.511966181094912e-05 1e-06 1e-08
-@value 8.789498023460432e-07 1e-06 1e-08
-@value 3.120463375997895e-07 1e-06 1e-08
-@value -6.585859961765525e-06 1e-06 1e-08
-@value -5.278694863250881e-06 1e-06 1e-08
+@value -6.3316727117524e-05 1e-05 1e-07
+@value -0.0002892063302319241 1e-05 1e-07
+@value 3.386768225102413e-05 1e-05 1e-07
+@value -2.510781673104479e-05 1e-05 1e-07
+@value -0.0001096911700833153 1e-05 1e-07
+@value                    0 1e-05 1e-07
+@value 1.711454621664259e-06 1e-05 1e-07
+@value -3.351830589750711e-06 1e-05 1e-07
+@value 9.249166349792779e-06 1e-05 1e-07
 Dictionary Key: shapey
-@value   0.5047742037931489 1e-06 1e-08
-@value   0.4308848253896001 1e-06 1e-08
-@value     0.41837894746838 1e-06 1e-08
-@value   0.3457799175046719 1e-06 1e-08
+@value   0.5047717967004901 1e-05 1e-07
+@value   0.4309207938255091 1e-05 1e-07
+@value   0.4183947877186315 1e-05 1e-07
+@value    0.345814593919071 1e-05 1e-07
 Dictionary Key: uin
-@value  0.01253095869698455 1e-06 1e-08
+@value  0.01253080468338332 1e-05 1e-07
 Dictionary Key: CMZ
 Dictionary Key: actuator
-@value -1.827321943504957e-05 1e-06 1e-08
-@value 1.680357887040057e-05 1e-06 1e-08
-@value 8.100367495627683e-06 1e-06 1e-08
-@value 1.703868644581847e-05 1e-06 1e-08
-@value 3.609939653385697e-05 1e-06 1e-08
-@value -1.870227962855834e-06 1e-06 1e-08
-@value -1.332374426799433e-07 1e-06 1e-08
-@value 1.694086925786985e-05 1e-06 1e-08
-@value 1.109040846829574e-05 1e-06 1e-08
+@value -5.021514640476469e-05 1e-05 1e-07
+@value 6.640353766706871e-05 1e-05 1e-07
+@value -8.446222825532045e-06 1e-05 1e-07
+@value 3.01884696257526e-05 1e-05 1e-07
+@value 0.0001366534329710487 1e-05 1e-07
+@value                    0 1e-05 1e-07
+@value -1.406133929283344e-07 1e-05 1e-07
+@value 1.619318007287018e-05 1e-05 1e-07
+@value -2.107448276873656e-05 1e-05 1e-07
 Dictionary Key: shapey
-@value   0.2668953339108849 1e-06 1e-08
-@value   0.2208847010983094 1e-06 1e-08
-@value    1.452914396105135 1e-06 1e-08
-@value    1.158474690326355 1e-06 1e-08
+@value   0.2668485334207251 1e-05 1e-07
+@value   0.2208426797545682 1e-05 1e-07
+@value     1.45290479365425 1e-05 1e-07
+@value    1.158460903211973 1e-05 1e-07
 Dictionary Key: uin
-@value 0.006644917645526382 1e-06 1e-08
+@value 0.006644788989934564 1e-05 1e-07
 Dictionary Key: VOL
 Dictionary Key: actuator
-@value  -0.5518169788072831 1e-06 1e-08
-@value  -0.1150050546497597 1e-06 1e-08
-@value -0.00169368387841708 1e-06 1e-08
-@value  0.08464197941469312 1e-06 1e-08
-@value  -0.1726869955797571 1e-06 1e-08
-@value -0.02412849805932089 1e-06 1e-08
-@value -0.0006253489347601414 1e-06 1e-08
-@value   0.1477203432297983 1e-06 1e-08
-@value    0.236558605470293 1e-06 1e-08
+@value   -1.493675689790086 1e-05 1e-07
+@value -0.03359611591182837 1e-05 1e-07
+@value -0.007784030820741375 1e-05 1e-07
+@value   0.0246815725573415 1e-05 1e-07
+@value  0.04670314361601848 1e-05 1e-07
+@value                    0 1e-05 1e-07
+@value -0.0005914311140623198 1e-05 1e-07
+@value  0.01787931746563437 1e-05 1e-07
+@value -0.01956468981121197 1e-05 1e-07
 Dictionary Key: shapey
-@value   -8492.333428661372 1e-06 1e-08
-@value   -7098.573845083894 1e-06 1e-08
-@value   -6231.933339038347 1e-06 1e-08
-@value   -5189.678537676995 1e-06 1e-08
+@value   -8492.405118996376 1e-05 1e-07
+@value   -7098.625585314998 1e-05 1e-07
+@value   -6231.987381713074 1e-05 1e-07
+@value   -5189.710248985367 1e-05 1e-07
 Dictionary Key: uin
-@value    102.4313185555929 1e-06 1e-08
+@value    102.4303895279213 1e-05 1e-07
 Dictionary Key: VOL1
 Dictionary Key: actuator
-@value -0.002026125984695204 1e-06 1e-08
-@value   0.1924343104940762 1e-06 1e-08
-@value 0.003007020967945589 1e-06 1e-08
-@value  -0.1397967402544465 1e-06 1e-08
-@value   0.3534887594602059 1e-06 1e-08
-@value  0.04484304955304086 1e-06 1e-08
-@value                    0 1e-06 1e-08
-@value  -0.2620354038912703 1e-06 1e-08
-@value  -0.4534208019908726 1e-06 1e-08
+@value 5.273559366969494e-16 1e-05 1e-07
+@value -3.816391647148976e-17 1e-05 1e-07
+@value -1.561251128379126e-16 1e-05 1e-07
+@value 4.60689390011058e-18 1e-05 1e-07
+@value 5.886685348839574e-16 1e-05 1e-07
+@value                    0 1e-05 1e-07
+@value                    0 1e-05 1e-07
+@value 2.02851108035083e-16 1e-05 1e-07
+@value 6.85058490472514e-17 1e-05 1e-07
 Dictionary Key: shapey
-@value -0.07467763617782404 1e-06 1e-08
-@value -0.06311909989631467 1e-06 1e-08
-@value -0.03815465875902022 1e-06 1e-08
-@value -0.03242364768470637 1e-06 1e-08
+@value  -0.1998373534061134 1e-05 1e-07
+@value  -0.1689067104724625 1e-05 1e-07
+@value  -0.1021018663252787 1e-05 1e-07
+@value -0.08676568076759897 1e-05 1e-07
 Dictionary Key: uin
-@value                    0 1e-06 1e-08
+@value                    0 1e-05 1e-07
 Dictionary Key: fail
-@value                    0 1e-06 1e-08
\ No newline at end of file
+@value                    0 1e-05 1e-07
\ No newline at end of file
diff --git a/tests/refs/DAFoam_Test_DARhoSimpleFoamMRFRef.txt b/tests/refs/DAFoam_Test_DARhoSimpleFoamMRFRef.txt
index b4719272..338f6292 100755
--- a/tests/refs/DAFoam_Test_DARhoSimpleFoamMRFRef.txt
+++ b/tests/refs/DAFoam_Test_DARhoSimpleFoamMRFRef.txt
@@ -4,14 +4,14 @@ Dictionary Key: fail
 @value                    0 1e-08 1e-10
 Dictionary Key: CMZ
 Dictionary Key: shapey
-@value  0.07016973276718444 1e-06 1e-08
-@value    0.140963828660477 1e-06 1e-08
-@value  0.08517780879100491 1e-06 1e-08
-@value   0.1245264598313216 1e-06 1e-08
+@value  0.07016973276718444 1e-05 1e-07
+@value    0.140963828660477 1e-05 1e-07
+@value  0.08517780879100491 1e-05 1e-07
+@value   0.1245264598313216 1e-05 1e-07
 Dictionary Key: shapez
-@value -0.009165942515949738 1e-06 1e-08
-@value -0.04507434388606746 1e-06 1e-08
-@value -0.04635882487560399 1e-06 1e-08
-@value -0.05734872722812122 1e-06 1e-08
+@value -0.009165942515949738 1e-05 1e-07
+@value -0.04507434388606746 1e-05 1e-07
+@value -0.04635882487560399 1e-05 1e-07
+@value -0.05734872722812122 1e-05 1e-07
 Dictionary Key: fail
-@value                    0 1e-06 1e-08
+@value                    0 1e-05 1e-07
diff --git a/tests/refs/DAFoam_Test_DARhoSimpleFoamRef.txt b/tests/refs/DAFoam_Test_DARhoSimpleFoamRef.txt
index 6e7905ab..80df3922 100755
--- a/tests/refs/DAFoam_Test_DARhoSimpleFoamRef.txt
+++ b/tests/refs/DAFoam_Test_DARhoSimpleFoamRef.txt
@@ -1,24 +1,24 @@
 Dictionary Key: CD
-@value  0.09340981962203246 1e-08 1e-10
+@value  0.09340977706079624 1e-08 1e-10
 Dictionary Key: CL
-@value   0.3122070733063254 1e-08 1e-10
+@value   0.3122067096074801 1e-08 1e-10
 Dictionary Key: fail
 @value                    0 1e-08 1e-10
 Dictionary Key: CD
 Dictionary Key: shapey
-@value   0.2116590327421694 1e-06 1e-08
-@value   0.1738848418621413 1e-06 1e-08
-@value    2.374417257561231 1e-06 1e-08
-@value      1.8835252312794 1e-06 1e-08
+@value   0.2140536273652476 1e-05 1e-07
+@value    0.177394058027215 1e-05 1e-07
+@value    2.375954185318922 1e-05 1e-07
+@value    1.885591206501376 1e-05 1e-07
 Dictionary Key: uin
-@value 0.003722184772337245 1e-06 1e-08
+@value 0.003915576327250028 1e-05 1e-07
 Dictionary Key: CL
 Dictionary Key: shapey
-@value   0.5456234649600328 1e-06 1e-08
-@value   0.4544910153001713 1e-06 1e-08
-@value    0.443337074425948 1e-06 1e-08
-@value   0.3585970307049681 1e-06 1e-08
+@value   0.5355584475236188 1e-05 1e-07
+@value   0.4393530067924477 1e-05 1e-07
+@value   0.4356534901534372 1e-05 1e-07
+@value   0.3464242397132455 1e-05 1e-07
 Dictionary Key: uin
-@value  0.01217123275855338 1e-06 1e-08
+@value   0.0125617487254271 1e-05 1e-07
 Dictionary Key: fail
-@value                    0 1e-06 1e-08
\ No newline at end of file
+@value                    0 1e-05 1e-07
\ No newline at end of file
diff --git a/tests/refs/DAFoam_Test_DARhoSimpleFoamUBendRef.txt b/tests/refs/DAFoam_Test_DARhoSimpleFoamUBendRef.txt
index bfd0dc83..a85f4754 100755
--- a/tests/refs/DAFoam_Test_DARhoSimpleFoamUBendRef.txt
+++ b/tests/refs/DAFoam_Test_DARhoSimpleFoamUBendRef.txt
@@ -6,21 +6,21 @@ Dictionary Key: fail
 @value                    0 1e-08 1e-10
 Dictionary Key: NU
 Dictionary Key: shapey
-@value    -134.236668925836 1e-06 1e-08
-@value    97.73028414379682 1e-06 1e-08
-@value   -82.21549764863623 1e-06 1e-08
+@value    -134.236668925836 1e-05 1e-07
+@value    97.73028414379682 1e-05 1e-07
+@value   -82.21549764863623 1e-05 1e-07
 Dictionary Key: shapez
-@value   -65.09444750369877 1e-06 1e-08
-@value   -107.9999149462616 1e-06 1e-08
-@value    79.59697519567609 1e-06 1e-08
+@value   -65.09444750369877 1e-05 1e-07
+@value   -107.9999149462616 1e-05 1e-07
+@value    79.59697519567609 1e-05 1e-07
 Dictionary Key: PL
 Dictionary Key: shapey
-@value    4.257880582642822 1e-06 1e-08
-@value    0.444819861890092 1e-06 1e-08
-@value  -0.3459501937887928 1e-06 1e-08
+@value    4.257880582642822 1e-05 1e-07
+@value    0.444819861890092 1e-05 1e-07
+@value  -0.3459501937887928 1e-05 1e-07
 Dictionary Key: shapez
-@value  0.07164971054744204 1e-06 1e-08
-@value  0.02175293132480229 1e-06 1e-08
-@value  -0.2156367726989875 1e-06 1e-08
+@value  0.07164971054744204 1e-05 1e-07
+@value  0.02175293132480229 1e-05 1e-07
+@value  -0.2156367726989875 1e-05 1e-07
 Dictionary Key: fail
-@value                    0 1e-06 1e-08
+@value                    0 1e-05 1e-07
diff --git a/tests/refs/DAFoam_Test_DASimpleFoamADRef.txt b/tests/refs/DAFoam_Test_DASimpleFoamADRef.txt
index 72da1d1a..f9adcc49 100755
--- a/tests/refs/DAFoam_Test_DASimpleFoamADRef.txt
+++ b/tests/refs/DAFoam_Test_DASimpleFoamADRef.txt
@@ -6,17 +6,17 @@ Dictionary Key: fail
 @value                    0 1e-08 1e-10
 Dictionary Key: CD
 Dictionary Key: alpha
-@value 0.002280322248925539 1e-06 1e-08
+@value 0.002280322248925539 1e-05 1e-07
 Dictionary Key: shapey
-@value -0.01063654962919052 1e-06 1e-08
-@value 0.005827183422422215 1e-06 1e-08
-@value  0.01999379830211091 1e-06 1e-08
+@value -0.01063654962919052 1e-05 1e-07
+@value 0.005827183422422215 1e-05 1e-07
+@value  0.01999379830211091 1e-05 1e-07
 Dictionary Key: CL
 Dictionary Key: alpha
-@value  0.08995513866376829 1e-06 1e-08
+@value  0.08995513866376829 1e-05 1e-07
 Dictionary Key: shapey
-@value   0.7008636067027021 1e-06 1e-08
-@value   0.6091514202242572 1e-06 1e-08
-@value    1.418731539899734 1e-06 1e-08
+@value   0.7008636067027021 1e-05 1e-07
+@value   0.6091514202242572 1e-05 1e-07
+@value    1.418731539899734 1e-05 1e-07
 Dictionary Key: fail
-@value                    0 1e-06 1e-08
\ No newline at end of file
+@value                    0 1e-05 1e-07
\ No newline at end of file
diff --git a/tests/refs/DAFoam_Test_DASimpleFoamMRFRef.txt b/tests/refs/DAFoam_Test_DASimpleFoamMRFRef.txt
index 8614ab1f..d9237d2c 100755
--- a/tests/refs/DAFoam_Test_DASimpleFoamMRFRef.txt
+++ b/tests/refs/DAFoam_Test_DASimpleFoamMRFRef.txt
@@ -4,14 +4,14 @@ Dictionary Key: fail
 @value                    0 1e-08 1e-10
 Dictionary Key: CMZ
 Dictionary Key: shapey
-@value 0.002301025727431101 1e-06 1e-08
-@value 0.004512120315371316 1e-06 1e-08
-@value   0.0025103380523812 1e-06 1e-08
-@value 0.005214120031159571 1e-06 1e-08
+@value 0.002301025727431101 1e-05 1e-07
+@value 0.004512120315371316 1e-05 1e-07
+@value   0.0025103380523812 1e-05 1e-07
+@value 0.005214120031159571 1e-05 1e-07
 Dictionary Key: shapez
-@value -0.0009424027326760953 1e-06 1e-08
-@value -0.001806512283893614 1e-06 1e-08
-@value -0.001508362837997657 1e-06 1e-08
-@value -0.002958130988623487 1e-06 1e-08
+@value -0.0009424027326760953 1e-05 1e-07
+@value -0.001806512283893614 1e-05 1e-07
+@value -0.001508362837997657 1e-05 1e-07
+@value -0.002958130988623487 1e-05 1e-07
 Dictionary Key: fail
-@value                    0 1e-06 1e-08
+@value                    0 1e-05 1e-07
diff --git a/tests/refs/DAFoam_Test_DASimpleFoamRef.txt b/tests/refs/DAFoam_Test_DASimpleFoamRef.txt
index e42c861e..ec3329f0 100755
--- a/tests/refs/DAFoam_Test_DASimpleFoamRef.txt
+++ b/tests/refs/DAFoam_Test_DASimpleFoamRef.txt
@@ -1,99 +1,99 @@
 Dictionary Key: CD
-@value  0.01438365115696073 1e-08 1e-10
+@value  0.01438365115696084 1e-08 1e-10
 Dictionary Key: CL
-@value    0.527843342329385 1e-08 1e-10
+@value   0.5278433423293855 1e-08 1e-10
 Dictionary Key: CMZ
-@value -0.006992993721841648 1e-08 1e-10
+@value -0.006992993721841563 1e-08 1e-10
 Dictionary Key: THRUST
 @value   0.3964124860392292 1e-08 1e-10
 Dictionary Key: VOL
-@value    32.90556883062945 1e-08 1e-10
+@value    32.90556883062804 1e-08 1e-10
 Dictionary Key: fail
 @value                    0 1e-08 1e-10
 Dictionary Key: CD
 Dictionary Key: actuator
-@value 0.002692654768137439 1e-06 1e-08
-@value -0.0003473342452621639 1e-06 1e-08
-@value 5.620233959624517e-05 1e-06 1e-08
-@value -0.005953704490659789 1e-06 1e-08
-@value 9.593962238332475e-05 1e-06 1e-08
-@value 1.956078532851308e-05 1e-06 1e-08
-@value 1.488603379413285e-08 1e-06 1e-08
-@value -0.001740961808881051 1e-06 1e-08
-@value -0.001285589183851513 1e-06 1e-08
+@value 0.002692654743062405 1e-05 1e-07
+@value -0.0003473341347664285 1e-05 1e-07
+@value 5.620234383570104e-05 1e-05 1e-07
+@value -0.005953704788967595 1e-05 1e-07
+@value 9.593947158077255e-05 1e-05 1e-07
+@value 1.956078536327928e-05 1e-05 1e-07
+@value 1.534919864800157e-08 1e-05 1e-07
+@value -0.001740961838225806 1e-05 1e-07
+@value -0.001285589164731539 1e-05 1e-07
 Dictionary Key: alpha
-@value 0.003478846532318931 1e-06 1e-08
+@value 0.003478846233720689 1e-05 1e-07
 Dictionary Key: shapey
-@value -0.01145880389935533 1e-06 1e-08
-@value  0.04946172103511462 1e-06 1e-08
-@value  0.09099507732318513 1e-06 1e-08
+@value -0.01145880278936309 1e-05 1e-07
+@value  0.04946171930909396 1e-05 1e-07
+@value  0.09099507726500972 1e-05 1e-07
 Dictionary Key: CL
 Dictionary Key: actuator
-@value -0.01775995690260076 1e-06 1e-08
-@value   0.1160533089312083 1e-06 1e-08
-@value 0.001883119174821481 1e-06 1e-08
-@value  -0.1581267552488027 1e-06 1e-08
-@value  -0.0343351422150087 1e-06 1e-08
-@value 0.000202711148420738 1e-06 1e-08
-@value -3.925629457013789e-07 1e-06 1e-08
-@value  -0.0280680262571186 1e-06 1e-08
-@value -0.005537899670178034 1e-06 1e-08
+@value -0.01775995579432492 1e-05 1e-07
+@value   0.1160533063360002 1e-05 1e-07
+@value  0.00188311916616678 1e-05 1e-07
+@value  -0.1581267547150706 1e-05 1e-07
+@value -0.03433514066432578 1e-05 1e-07
+@value 0.0002027111536501591 1e-05 1e-07
+@value -8.172073868387086e-07 1e-05 1e-07
+@value -0.02806802638939627 1e-05 1e-07
+@value -0.005537900303758031 1e-05 1e-07
 Dictionary Key: alpha
-@value  0.09973980338663201 1e-06 1e-08
+@value  0.09973980264096334 1e-05 1e-07
 Dictionary Key: shapey
-@value    1.559462973905275 1e-06 1e-08
-@value    1.231602815780193 1e-06 1e-08
-@value    1.803087982885234 1e-06 1e-08
+@value    1.559463012159858 1e-05 1e-07
+@value    1.231602807591228 1e-05 1e-07
+@value    1.803088011202189 1e-05 1e-07
 Dictionary Key: CMZ
 Dictionary Key: actuator
-@value -0.001714635670651376 1e-06 1e-08
-@value -0.0005710087869660589 1e-06 1e-08
-@value 0.0001053970903022406 1e-06 1e-08
-@value -0.005972163583780316 1e-06 1e-08
-@value 0.0002894110032041877 1e-06 1e-08
-@value -1.652421277542231e-05 1e-06 1e-08
-@value -7.316302326092626e-08 1e-06 1e-08
-@value 0.0004079648918291139 1e-06 1e-08
-@value 0.001743591499191397 1e-06 1e-08
+@value -0.001714635571617953 1e-05 1e-07
+@value -0.0005710092451789862 1e-05 1e-07
+@value 0.0001053970922245933 1e-05 1e-07
+@value -0.005972163653488304 1e-05 1e-07
+@value 0.0002894111646713729 1e-05 1e-07
+@value -1.652421307341438e-05 1e-05 1e-07
+@value -1.640852649479966e-07 1e-05 1e-07
+@value 0.0004079649174387717 1e-05 1e-07
+@value 0.001743591514138321 1e-05 1e-07
 Dictionary Key: alpha
-@value -0.002527511590113433 1e-06 1e-08
+@value -0.00252751197470288 1e-05 1e-07
 Dictionary Key: shapey
-@value  0.04277114199161391 1e-06 1e-08
-@value   0.3266475026826117 1e-06 1e-08
-@value   0.7983250954537272 1e-06 1e-08
+@value  0.04277114768660325 1e-05 1e-07
+@value   0.3266475035683201 1e-05 1e-07
+@value   0.7983250993983276 1e-05 1e-07
 Dictionary Key: THRUST
 Dictionary Key: actuator
-@value   0.3141086102615986 1e-06 1e-08
-@value -0.003605129121397876 1e-06 1e-08
-@value 0.007310727357323632 1e-06 1e-08
-@value   -0.819670401731476 1e-06 1e-08
-@value   0.8428678211159779 1e-06 1e-08
-@value 0.003964124860367235 1e-06 1e-08
-@value                    0 1e-06 1e-08
-@value  -0.2740304202085708 1e-06 1e-08
-@value  -0.3409006479776489 1e-06 1e-08
+@value   0.3141086102615986 1e-05 1e-07
+@value -0.003605129121397876 1e-05 1e-07
+@value 0.007310727357323632 1e-05 1e-07
+@value   -0.819670401731476 1e-05 1e-07
+@value   0.8428678211159779 1e-05 1e-07
+@value 0.003964124860367235 1e-05 1e-07
+@value                    0 1e-05 1e-07
+@value  -0.2740304202085708 1e-05 1e-07
+@value  -0.3409006479776489 1e-05 1e-07
 Dictionary Key: alpha
-@value                    0 1e-06 1e-08
+@value                    0 1e-05 1e-07
 Dictionary Key: shapey
-@value -0.009188209263988334 1e-06 1e-08
-@value   0.0006339731860594 1e-06 1e-08
-@value 0.0007674441613869654 1e-06 1e-08
+@value -0.009188209263988334 1e-05 1e-07
+@value   0.0006339731860594 1e-05 1e-07
+@value 0.0007674441613869654 1e-05 1e-07
 Dictionary Key: VOL
 Dictionary Key: actuator
-@value   -1.789350133112099 1e-06 1e-08
-@value    11.26830274939814 1e-06 1e-08
-@value   0.2116803131173961 1e-06 1e-08
-@value   -18.33919531649438 1e-06 1e-08
-@value    -2.83516783357151 1e-06 1e-08
-@value  0.03030092792978192 1e-06 1e-08
-@value -3.793564764374215e-05 1e-06 1e-08
-@value   -3.581283353883602 1e-06 1e-08
-@value   -1.311124290755679 1e-06 1e-08
+@value   -1.789350017581762 1e-05 1e-07
+@value    11.26830256393616 1e-05 1e-07
+@value   0.2116803123864702 1e-05 1e-07
+@value   -18.33919528265704 1e-05 1e-07
+@value   -2.835167655956745 1e-05 1e-07
+@value  0.03030092859457912 1e-05 1e-07
+@value -7.666586571084363e-05 1e-05 1e-07
+@value   -3.581283376190157 1e-05 1e-07
+@value   -1.311124366909558 1e-05 1e-07
 Dictionary Key: alpha
-@value    10.47559305394806 1e-06 1e-08
+@value    10.47559304035274 1e-05 1e-07
 Dictionary Key: shapey
-@value    213.3053844308212 1e-06 1e-08
-@value    145.9822627702432 1e-06 1e-08
-@value     168.877481704946 1e-06 1e-08
+@value    213.3053877790166 1e-05 1e-07
+@value    145.9822612662322 1e-05 1e-07
+@value      168.87748437004 1e-05 1e-07
 Dictionary Key: fail
-@value                    0 1e-06 1e-08
\ No newline at end of file
+@value                    0 1e-05 1e-07
\ No newline at end of file
diff --git a/tests/refs/DAFoam_Test_DASimpleTFoamRef.txt b/tests/refs/DAFoam_Test_DASimpleTFoamRef.txt
index 3548ed6b..6875cbe3 100755
--- a/tests/refs/DAFoam_Test_DASimpleTFoamRef.txt
+++ b/tests/refs/DAFoam_Test_DASimpleTFoamRef.txt
@@ -6,21 +6,21 @@ Dictionary Key: fail
 @value                    0 1e-08 1e-10
 Dictionary Key: NU
 Dictionary Key: shapey
-@value   -195.4862610369968 1e-06 1e-08
-@value    67.25621608243864 1e-06 1e-08
-@value   -42.73188419356157 1e-06 1e-08
+@value   -195.4862610369968 1e-05 1e-07
+@value    67.25621608243864 1e-05 1e-07
+@value   -42.73188419356157 1e-05 1e-07
 Dictionary Key: shapez
-@value   -4.219438020966073 1e-06 1e-08
-@value   -1.333434004439317 1e-06 1e-08
-@value     1.94980915347223 1e-06 1e-08
+@value   -4.219438020966073 1e-05 1e-07
+@value   -1.333434004439317 1e-05 1e-07
+@value     1.94980915347223 1e-05 1e-07
 Dictionary Key: PL
 Dictionary Key: shapey
-@value    2.115930871171957 1e-06 1e-08
-@value  -0.7117232563028599 1e-06 1e-08
-@value  -0.3791625234047521 1e-06 1e-08
+@value    2.115930871171957 1e-05 1e-07
+@value  -0.7117232563028599 1e-05 1e-07
+@value  -0.3791625234047521 1e-05 1e-07
 Dictionary Key: shapez
-@value -0.02150447850407335 1e-06 1e-08
-@value  0.04788112027532705 1e-06 1e-08
-@value  0.02242263381112408 1e-06 1e-08
+@value -0.02150447850407335 1e-05 1e-07
+@value  0.04788112027532705 1e-05 1e-07
+@value  0.02242263381112408 1e-05 1e-07
 Dictionary Key: fail
-@value                    0 1e-06 1e-08
\ No newline at end of file
+@value                    0 1e-05 1e-07
\ No newline at end of file
diff --git a/tests/refs/DAFoam_Test_DASolidDisplacementFoamRef.txt b/tests/refs/DAFoam_Test_DASolidDisplacementFoamRef.txt
index 9598d559..2d55ca86 100755
--- a/tests/refs/DAFoam_Test_DASolidDisplacementFoamRef.txt
+++ b/tests/refs/DAFoam_Test_DASolidDisplacementFoamRef.txt
@@ -6,21 +6,21 @@ Dictionary Key: fail
 @value                    0 1e-08 1e-10
 Dictionary Key: M
 Dictionary Key: shapex
-@value   -134.4036118061922 1e-06 1e-08
-@value   -355.6352710656938 1e-06 1e-08
-@value    -134.317198273493 1e-06 1e-08
+@value   -134.4036118061922 1e-05 1e-07
+@value   -355.6352710656938 1e-05 1e-07
+@value    -134.317198273493 1e-05 1e-07
 Dictionary Key: shapey
-@value     133.578083714383 1e-06 1e-08
-@value    351.9087685690465 1e-06 1e-08
-@value    133.8341984392173 1e-06 1e-08
+@value     133.578083714383 1e-05 1e-07
+@value    351.9087685690465 1e-05 1e-07
+@value    133.8341984392173 1e-05 1e-07
 Dictionary Key: VMS
 Dictionary Key: shapex
-@value   -992.0355945685246 1e-06 1e-08
-@value   -2602.054125021486 1e-06 1e-08
-@value   -1269.444213538443 1e-06 1e-08
+@value   -992.0355945685246 1e-05 1e-07
+@value   -2602.054125021486 1e-05 1e-07
+@value   -1269.444213538443 1e-05 1e-07
 Dictionary Key: shapey
-@value    -734.173963930622 1e-06 1e-08
-@value   -6354.753651965501 1e-06 1e-08
-@value   -1169.305994848094 1e-06 1e-08
+@value    -734.173963930622 1e-05 1e-07
+@value   -6354.753651965501 1e-05 1e-07
+@value   -1169.305994848094 1e-05 1e-07
 Dictionary Key: fail
-@value                    0 1e-06 1e-08
+@value                    0 1e-05 1e-07
diff --git a/tests/refs/DAFoam_Test_DATurboFoamSubsonicRef.txt b/tests/refs/DAFoam_Test_DATurboFoamSubsonicRef.txt
index dec32442..8290cddb 100755
--- a/tests/refs/DAFoam_Test_DATurboFoamSubsonicRef.txt
+++ b/tests/refs/DAFoam_Test_DATurboFoamSubsonicRef.txt
@@ -6,25 +6,25 @@ Dictionary Key: fail
 @value                    0 1e-08 1e-10
 Dictionary Key: CMZ
 Dictionary Key: shapey
-@value   0.2847715919611993 1e-06 1e-08
-@value   0.5020122841985006 1e-06 1e-08
-@value    0.339989430432045 1e-06 1e-08
-@value   0.4471545417329905 1e-06 1e-08
+@value   0.2847715919611993 1e-05 1e-07
+@value   0.5020122841985006 1e-05 1e-07
+@value    0.339989430432045 1e-05 1e-07
+@value   0.4471545417329905 1e-05 1e-07
 Dictionary Key: shapez
-@value -0.03754549250758193 1e-06 1e-08
-@value  -0.1668372689661463 1e-06 1e-08
-@value  -0.1865409331445353 1e-06 1e-08
-@value  -0.2092364378494078 1e-06 1e-08
+@value -0.03754549250758193 1e-05 1e-07
+@value  -0.1668372689661463 1e-05 1e-07
+@value  -0.1865409331445353 1e-05 1e-07
+@value  -0.2092364378494078 1e-05 1e-07
 Dictionary Key: TPR
 Dictionary Key: shapey
-@value  0.08984178060879607 1e-06 1e-08
-@value  -0.1026040687812797 1e-06 1e-08
-@value  0.07889426252189255 1e-06 1e-08
-@value -0.08460343368551185 1e-06 1e-08
+@value  0.08984178060879607 1e-05 1e-07
+@value  -0.1026040687812797 1e-05 1e-07
+@value  0.07889426252189255 1e-05 1e-07
+@value -0.08460343368551185 1e-05 1e-07
 Dictionary Key: shapez
-@value -0.03253669585379524 1e-06 1e-08
-@value  0.09552686633819965 1e-06 1e-08
-@value -0.04523225304246882 1e-06 1e-08
-@value   0.1038329607242777 1e-06 1e-08
+@value -0.03253669585379524 1e-05 1e-07
+@value  0.09552686633819965 1e-05 1e-07
+@value -0.04523225304246882 1e-05 1e-07
+@value   0.1038329607242777 1e-05 1e-07
 Dictionary Key: fail
-@value                    0 1e-06 1e-08
+@value                    0 1e-05 1e-07
diff --git a/tests/refs/DAFoam_Test_DATurboFoamTransonicRef.txt b/tests/refs/DAFoam_Test_DATurboFoamTransonicRef.txt
index 299497b5..571dd92d 100755
--- a/tests/refs/DAFoam_Test_DATurboFoamTransonicRef.txt
+++ b/tests/refs/DAFoam_Test_DATurboFoamTransonicRef.txt
@@ -10,47 +10,47 @@ Dictionary Key: fail
 @value                    0 1e-08 1e-10
 Dictionary Key: CMZ
 Dictionary Key: shapey
-@value   0.6110279328980447 1e-06 1e-08
-@value   0.6148742918649588 1e-06 1e-08
-@value    0.825383724754519 1e-06 1e-08
-@value   0.9500487157171859 1e-06 1e-08
+@value   0.6110279328980447 1e-05 1e-07
+@value   0.6148742918649588 1e-05 1e-07
+@value    0.825383724754519 1e-05 1e-07
+@value   0.9500487157171859 1e-05 1e-07
 Dictionary Key: shapez
-@value  -0.2517378087598814 1e-06 1e-08
-@value  -0.2953069289721815 1e-06 1e-08
-@value  -0.5415860339601032 1e-06 1e-08
-@value  -0.6629720291206106 1e-06 1e-08
+@value  -0.2517378087598814 1e-05 1e-07
+@value  -0.2953069289721815 1e-05 1e-07
+@value  -0.5415860339601032 1e-05 1e-07
+@value  -0.6629720291206106 1e-05 1e-07
 Dictionary Key: MFR
 Dictionary Key: shapey
-@value   0.3507757164928561 1e-06 1e-08
-@value   -2.812319413552892 1e-06 1e-08
-@value   0.4673931240533841 1e-06 1e-08
-@value   -2.919343629121333 1e-06 1e-08
+@value   0.3507757164928561 1e-05 1e-07
+@value   -2.812319413552892 1e-05 1e-07
+@value   0.4673931240533841 1e-05 1e-07
+@value   -2.919343629121333 1e-05 1e-07
 Dictionary Key: shapez
-@value -0.09507540313568341 1e-06 1e-08
-@value    1.876175512638437 1e-06 1e-08
-@value  -0.1360574716620557 1e-06 1e-08
-@value    2.365042657590311 1e-06 1e-08
+@value -0.09507540313568341 1e-05 1e-07
+@value    1.876175512638437 1e-05 1e-07
+@value  -0.1360574716620557 1e-05 1e-07
+@value    2.365042657590311 1e-05 1e-07
 Dictionary Key: TPR
 Dictionary Key: shapey
-@value   0.1850144544385676 1e-06 1e-08
-@value    0.289895040201579 1e-06 1e-08
-@value   0.1988987338061133 1e-06 1e-08
-@value   0.3453494413683635 1e-06 1e-08
+@value   0.1850144544385676 1e-05 1e-07
+@value    0.289895040201579 1e-05 1e-07
+@value   0.1988987338061133 1e-05 1e-07
+@value   0.3453494413683635 1e-05 1e-07
 Dictionary Key: shapez
-@value  -0.1030992221239914 1e-06 1e-08
-@value  -0.1591277492045404 1e-06 1e-08
-@value  -0.1547827142144216 1e-06 1e-08
-@value  -0.2571254833694371 1e-06 1e-08
+@value  -0.1030992221239914 1e-05 1e-07
+@value  -0.1591277492045404 1e-05 1e-07
+@value  -0.1547827142144216 1e-05 1e-07
+@value  -0.2571254833694371 1e-05 1e-07
 Dictionary Key: TTR
 Dictionary Key: shapey
-@value  0.06423922290933609 1e-06 1e-08
-@value    0.167684266522984 1e-06 1e-08
-@value  0.06517581885047612 1e-06 1e-08
-@value   0.1859748534532155 1e-06 1e-08
+@value  0.06423922290933609 1e-05 1e-07
+@value    0.167684266522984 1e-05 1e-07
+@value  0.06517581885047612 1e-05 1e-07
+@value   0.1859748534532155 1e-05 1e-07
 Dictionary Key: shapez
-@value -0.02270256867201838 1e-06 1e-08
-@value -0.06914072490572683 1e-06 1e-08
-@value -0.03549867558355561 1e-06 1e-08
-@value  -0.1125887416832533 1e-06 1e-08
+@value -0.02270256867201838 1e-05 1e-07
+@value -0.06914072490572683 1e-05 1e-07
+@value -0.03549867558355561 1e-05 1e-07
+@value  -0.1125887416832533 1e-05 1e-07
 Dictionary Key: fail
-@value                    0 1e-06 1e-08
+@value                    0 1e-05 1e-07
diff --git a/tests/refs/DAFoam_Test_IntegrationRef.txt b/tests/refs/DAFoam_Test_IntegrationRef.txt
index 58a4f363..6d13927a 100755
--- a/tests/refs/DAFoam_Test_IntegrationRef.txt
+++ b/tests/refs/DAFoam_Test_IntegrationRef.txt
@@ -1,23 +1,23 @@
 Dictionary Key: alpha
-@value    4.983717284754065 1e-06 1e-08
+@value    4.983717284754065 1e-05 1e-07
 Dictionary Key: shapey
-@value -0.007921638247074878 1e-06 1e-08
-@value -0.007921638247074876 1e-06 1e-08
-@value 0.007921638247074876 1e-06 1e-08
-@value 0.007921638247074883 1e-06 1e-08
-@value -0.03828251157381521 1e-06 1e-08
-@value  -0.0382825115738152 1e-06 1e-08
-@value  0.01296166970151721 1e-06 1e-08
-@value  0.01296166970151721 1e-06 1e-08
-@value -0.01007603259183909 1e-06 1e-08
-@value -0.01007603259183909 1e-06 1e-08
-@value 0.006776110782364444 1e-06 1e-08
-@value 0.006776110782364448 1e-06 1e-08
-@value -0.006275226705233793 1e-06 1e-08
-@value -0.006275226705233784 1e-06 1e-08
-@value 0.006469684027699906 1e-06 1e-08
-@value 0.006469684027699912 1e-06 1e-08
-@value -0.001009412363331983 1e-06 1e-08
-@value -0.001009412363331989 1e-06 1e-08
-@value 0.001009412363331983 1e-06 1e-08
-@value 0.001009412363331984 1e-06 1e-08
\ No newline at end of file
+@value -0.007921638247074878 1e-05 1e-07
+@value -0.007921638247074876 1e-05 1e-07
+@value 0.007921638247074876 1e-05 1e-07
+@value 0.007921638247074883 1e-05 1e-07
+@value -0.03828251157381521 1e-05 1e-07
+@value  -0.0382825115738152 1e-05 1e-07
+@value  0.01296166970151721 1e-05 1e-07
+@value  0.01296166970151721 1e-05 1e-07
+@value -0.01007603259183909 1e-05 1e-07
+@value -0.01007603259183909 1e-05 1e-07
+@value 0.006776110782364444 1e-05 1e-07
+@value 0.006776110782364448 1e-05 1e-07
+@value -0.006275226705233793 1e-05 1e-07
+@value -0.006275226705233784 1e-05 1e-07
+@value 0.006469684027699906 1e-05 1e-07
+@value 0.006469684027699912 1e-05 1e-07
+@value -0.001009412363331983 1e-05 1e-07
+@value -0.001009412363331989 1e-05 1e-07
+@value 0.001009412363331983 1e-05 1e-07
+@value 0.001009412363331984 1e-05 1e-07
\ No newline at end of file
diff --git a/tests/runTests_DAPisoFoam.py b/tests/runTests_DAPisoFoam.py
index a70d44e6..89526b36 100755
--- a/tests/runTests_DAPisoFoam.py
+++ b/tests/runTests_DAPisoFoam.py
@@ -36,7 +36,7 @@
     "solverName": "DAPisoFoam",
     "designSurfaceFamily": "designSurface",
     "designSurfaces": ["wallsbump"],
-    "hybridAdjoint": {"active": True, "nTimeInstances": 3, "periodicity": 1.0},
+    "unsteadyAdjoint": {"mode": "hybridAdjoint", "nTimeInstances": 3, "periodicity": 1.0},
     "intmdVar" : {
          "UMean" : {
              "operation": "Mean",
@@ -186,8 +186,8 @@ def actuator(val, geo):
 DVCon.setSurface(surf)
 
 # optFuncs
-def setHybridAdjointObjFuncs(DASolver, funcs, evalFuncs):
-    nTimeInstances = DASolver.getOption("hybridAdjoint")["nTimeInstances"]
+def setObjFuncsUnsteady(DASolver, funcs, evalFuncs):
+    nTimeInstances = DASolver.getOption("unsteadyAdjoint")["nTimeInstances"]
     for func in evalFuncs:
         avgObjVal = 0.0
         for i in range(nTimeInstances):
@@ -197,7 +197,7 @@ def setHybridAdjointObjFuncs(DASolver, funcs, evalFuncs):
     funcs["fail"] = False
 
 
-def setHybridAdjointObjFuncsSens(CFDSolver, funcs, funcsSensAllTimeInstances, funcsSensCombined):
+def setObjFuncsSensUnsteady(CFDSolver, funcs, funcsSensAllTimeInstances, funcsSensCombined):
 
     nTimeInstances = 1.0 * len(funcsSensAllTimeInstances)
     for funcsSens in funcsSensAllTimeInstances:
@@ -225,19 +225,19 @@ def setHybridAdjointObjFuncsSens(CFDSolver, funcs, funcsSensAllTimeInstances, fu
 optFuncs.DVCon = DVCon
 optFuncs.evalFuncs = evalFuncs
 optFuncs.gcomm = gcomm
-optFuncs.setHybridAdjointObjFuncs = setHybridAdjointObjFuncs
-optFuncs.setHybridAdjointObjFuncsSens = setHybridAdjointObjFuncsSens
+optFuncs.setObjFuncsUnsteady = setObjFuncsUnsteady
+optFuncs.setObjFuncsSensUnsteady = setObjFuncsSensUnsteady
 
 # Run
 if calcFDSens == 1:
-    optFuncs.calcFDSens(objFun=optFuncs.calcObjFuncValuesHybridAdjoint, fileName="sensFD.txt")
+    optFuncs.calcFDSens(objFun=optFuncs.calcObjFuncValuesUnsteady, fileName="sensFD.txt")
 else:
     DASolver.runColoring()
     xDV = DVGeo.getValues()
     funcs = {}
-    funcs, fail = optFuncs.calcObjFuncValuesHybridAdjoint(xDV)
+    funcs, fail = optFuncs.calcObjFuncValuesUnsteady(xDV)
     funcsSens = {}
-    funcsSens, fail = optFuncs.calcObjFuncSensHybridAdjoint(xDV, funcs)
+    funcsSens, fail = optFuncs.calcObjFuncSensUnsteady(xDV, funcs)
     if gcomm.rank == 0:
         reg_write_dict(funcs, 1e-8, 1e-10)
-        reg_write_dict(funcsSens, 1e-6, 1e-8)
+        reg_write_dict(funcsSens, 1e-5, 1e-7)
diff --git a/tests/runTests_DAPisoFoamACTL.py b/tests/runTests_DAPisoFoamACTL.py
index 2ef6342a..98d043b3 100755
--- a/tests/runTests_DAPisoFoamACTL.py
+++ b/tests/runTests_DAPisoFoamACTL.py
@@ -37,7 +37,7 @@
     "designSurfaceFamily": "designSurface",
     "designSurfaces": ["wallsbump"],
     "adjPCLag": 3,
-    "hybridAdjoint": {"active": True, "nTimeInstances": 3, "periodicity": 1.0},
+    "unsteadyAdjoint": {"mode": "hybridAdjoint", "nTimeInstances": 3, "periodicity": 1.0},
     "intmdVar" : {
          "UMean" : {
              "operation": "Mean",
@@ -189,8 +189,8 @@ def actuator(val, geo):
 DVCon.setSurface(surf)
 
 # optFuncs
-def setHybridAdjointObjFuncs(DASolver, funcs, evalFuncs):
-    nTimeInstances = DASolver.getOption("hybridAdjoint")["nTimeInstances"]
+def setObjFuncsUnsteady(DASolver, funcs, evalFuncs):
+    nTimeInstances = DASolver.getOption("unsteadyAdjoint")["nTimeInstances"]
     for func in evalFuncs:
         avgObjVal = 0.0
         for i in range(nTimeInstances):
@@ -200,7 +200,7 @@ def setHybridAdjointObjFuncs(DASolver, funcs, evalFuncs):
     funcs["fail"] = False
 
 
-def setHybridAdjointObjFuncsSens(CFDSolver, funcs, funcsSensAllTimeInstances, funcsSensCombined):
+def setObjFuncsSensUnsteady(CFDSolver, funcs, funcsSensAllTimeInstances, funcsSensCombined):
 
     nTimeInstances = 1.0 * len(funcsSensAllTimeInstances)
     for funcsSens in funcsSensAllTimeInstances:
@@ -228,19 +228,19 @@ def setHybridAdjointObjFuncsSens(CFDSolver, funcs, funcsSensAllTimeInstances, fu
 optFuncs.DVCon = DVCon
 optFuncs.evalFuncs = evalFuncs
 optFuncs.gcomm = gcomm
-optFuncs.setHybridAdjointObjFuncs = setHybridAdjointObjFuncs
-optFuncs.setHybridAdjointObjFuncsSens = setHybridAdjointObjFuncsSens
+optFuncs.setObjFuncsUnsteady = setObjFuncsUnsteady
+optFuncs.setObjFuncsSensUnsteady = setObjFuncsSensUnsteady
 
 # Run
 if calcFDSens == 1:
-    optFuncs.calcFDSens(objFun=optFuncs.calcObjFuncValuesHybridAdjoint, fileName="sensFD.txt")
+    optFuncs.calcFDSens(objFun=optFuncs.calcObjFuncValuesUnsteady, fileName="sensFD.txt")
 else:
     DASolver.runColoring()
     xDV = DVGeo.getValues()
     funcs = {}
-    funcs, fail = optFuncs.calcObjFuncValuesHybridAdjoint(xDV)
+    funcs, fail = optFuncs.calcObjFuncValuesUnsteady(xDV)
     funcsSens = {}
-    funcsSens, fail = optFuncs.calcObjFuncSensHybridAdjoint(xDV, funcs)
+    funcsSens, fail = optFuncs.calcObjFuncSensUnsteady(xDV, funcs)
     if gcomm.rank == 0:
         reg_write_dict(funcs, 1e-8, 1e-10)
-        reg_write_dict(funcsSens, 1e-6, 1e-8)
+        reg_write_dict(funcsSens, 1e-5, 1e-7)
diff --git a/tests/runTests_DARhoSimpleCFoam.py b/tests/runTests_DARhoSimpleCFoam.py
index 496ffc7f..68fdd565 100755
--- a/tests/runTests_DARhoSimpleCFoam.py
+++ b/tests/runTests_DARhoSimpleCFoam.py
@@ -165,5 +165,5 @@ def alpha(val, geo):
     funcsSens, fail = optFuncs.calcObjFuncSens(xDV, funcs)
     if gcomm.rank == 0:
         reg_write_dict(funcs, 1e-8, 1e-10)
-        reg_write_dict(funcsSens, 1e-6, 1e-8)
+        reg_write_dict(funcsSens, 1e-5, 1e-7)
 
diff --git a/tests/runTests_DARhoSimpleCFoamAD.py b/tests/runTests_DARhoSimpleCFoamAD.py
index 3c77254e..a944c56b 100755
--- a/tests/runTests_DARhoSimpleCFoamAD.py
+++ b/tests/runTests_DARhoSimpleCFoamAD.py
@@ -166,5 +166,5 @@ def alpha(val, geo):
     funcsSens, fail = optFuncs.calcObjFuncSens(xDV, funcs)
     if gcomm.rank == 0:
         reg_write_dict(funcs, 1e-8, 1e-10)
-        reg_write_dict(funcsSens, 1e-6, 1e-8)
+        reg_write_dict(funcsSens, 1e-5, 1e-7)
 
diff --git a/tests/runTests_DARhoSimpleFoam.py b/tests/runTests_DARhoSimpleFoam.py
index daf33726..06c7bc56 100755
--- a/tests/runTests_DARhoSimpleFoam.py
+++ b/tests/runTests_DARhoSimpleFoam.py
@@ -186,7 +186,7 @@ def uin(val, geo):
     funcsSens, fail = optFuncs.calcObjFuncSens(xDV, funcs)
     if gcomm.rank == 0:
         reg_write_dict(funcs, 1e-8, 1e-10)
-        reg_write_dict(funcsSens, 1e-6, 1e-8)
+        reg_write_dict(funcsSens, 1e-5, 1e-7)
 
 
 # *************************************************************
diff --git a/tests/runTests_DARhoSimpleFoamAD.py b/tests/runTests_DARhoSimpleFoamAD.py
index 905cd022..73f89e60 100755
--- a/tests/runTests_DARhoSimpleFoamAD.py
+++ b/tests/runTests_DARhoSimpleFoamAD.py
@@ -79,6 +79,8 @@
             "eps": 0.1,
             "expM": 1.0,
             "expN": 0.5,
+            "adjustThrust": 1,
+            "targetThrust": 1.2
         },
     },
     "objFunc": {
@@ -222,6 +224,8 @@ def actuator(val, geo):
                 "eps": 0.1,  # eps should be of cell size
                 "expM": actExpM,
                 "expN": actExpN,
+                "adjustThrust": 1,
+                "targetThrust": 1.2
             },
         },
     )
@@ -281,4 +285,4 @@ def actuator(val, geo):
     funcsSens, fail = optFuncs.calcObjFuncSens(xDV, funcs)
     if gcomm.rank == 0:
         reg_write_dict(funcs, 1e-8, 1e-10)
-        reg_write_dict(funcsSens, 1e-6, 1e-8)
+        reg_write_dict(funcsSens, 1e-5, 1e-7)
diff --git a/tests/runTests_DARhoSimpleFoamMRF.py b/tests/runTests_DARhoSimpleFoamMRF.py
index 57469eb6..b4a039d7 100755
--- a/tests/runTests_DARhoSimpleFoamMRF.py
+++ b/tests/runTests_DARhoSimpleFoamMRF.py
@@ -128,4 +128,4 @@
     funcsSens, fail = optFuncs.calcObjFuncSens(xDV, funcs)
     if gcomm.rank == 0:
         reg_write_dict(funcs, 1e-8, 1e-10)
-        reg_write_dict(funcsSens, 1e-6, 1e-8)
+        reg_write_dict(funcsSens, 1e-5, 1e-7)
diff --git a/tests/runTests_DARhoSimpleFoamUBend.py b/tests/runTests_DARhoSimpleFoamUBend.py
index f426c5b0..dfb2c3bc 100755
--- a/tests/runTests_DARhoSimpleFoamUBend.py
+++ b/tests/runTests_DARhoSimpleFoamUBend.py
@@ -130,4 +130,4 @@
     funcsSens, fail = optFuncs.calcObjFuncSens(xDV, funcs)
     if gcomm.rank == 0:
         reg_write_dict(funcs, 1e-8, 1e-10)
-        reg_write_dict(funcsSens, 1e-6, 1e-8)
+        reg_write_dict(funcsSens, 1e-5, 1e-7)
diff --git a/tests/runTests_DASimpleFoam.py b/tests/runTests_DASimpleFoam.py
index 520a7a13..e74d2bda 100755
--- a/tests/runTests_DASimpleFoam.py
+++ b/tests/runTests_DASimpleFoam.py
@@ -65,6 +65,7 @@
             "eps": 0.1,  # eps should be of cell size
             "expM": 1.0,
             "expN": 0.5,
+            "adjustThrust": 0,
         },
     },
     "objFunc": {
@@ -190,6 +191,7 @@ def actuator(val, geo):
                 "eps": 0.1,  # eps should be of cell size
                 "expM": actExpM,
                 "expN": actExpN,
+                "adjustThrust": 0,
             },
         },
     )
@@ -249,4 +251,4 @@ def actuator(val, geo):
     funcsSens, fail = optFuncs.calcObjFuncSens(xDV, funcs)
     if gcomm.rank == 0:
         reg_write_dict(funcs, 1e-8, 1e-10)
-        reg_write_dict(funcsSens, 1e-6, 1e-8)
+        reg_write_dict(funcsSens, 1e-5, 1e-7)
diff --git a/tests/runTests_DASimpleFoamAD.py b/tests/runTests_DASimpleFoamAD.py
index 6834c13e..aedbbe25 100755
--- a/tests/runTests_DASimpleFoamAD.py
+++ b/tests/runTests_DASimpleFoamAD.py
@@ -151,4 +151,4 @@ def alpha(val, geo):
     funcsSens, fail = optFuncs.calcObjFuncSens(xDV, funcs)
     if gcomm.rank == 0:
         reg_write_dict(funcs, 1e-8, 1e-10)
-        reg_write_dict(funcsSens, 1e-6, 1e-8)
+        reg_write_dict(funcsSens, 1e-5, 1e-7)
diff --git a/tests/runTests_DASimpleFoamMRF.py b/tests/runTests_DASimpleFoamMRF.py
index 783c9107..ef76340a 100755
--- a/tests/runTests_DASimpleFoamMRF.py
+++ b/tests/runTests_DASimpleFoamMRF.py
@@ -115,4 +115,4 @@
     funcsSens, fail = optFuncs.calcObjFuncSens(xDV, funcs)
     if gcomm.rank == 0:
         reg_write_dict(funcs, 1e-8, 1e-10)
-        reg_write_dict(funcsSens, 1e-6, 1e-8)
+        reg_write_dict(funcsSens, 1e-5, 1e-7)
diff --git a/tests/runTests_DASimpleTFoam.py b/tests/runTests_DASimpleTFoam.py
index 46bd1ad3..52b358b0 100755
--- a/tests/runTests_DASimpleTFoam.py
+++ b/tests/runTests_DASimpleTFoam.py
@@ -138,4 +138,4 @@
     funcsSens, fail = optFuncs.calcObjFuncSens(xDV, funcs)
     if gcomm.rank == 0:
         reg_write_dict(funcs, 1e-8, 1e-10)
-        reg_write_dict(funcsSens, 1e-6, 1e-8)
+        reg_write_dict(funcsSens, 1e-5, 1e-7)
diff --git a/tests/runTests_DASolidDisplacementFoam.py b/tests/runTests_DASolidDisplacementFoam.py
index 3840582d..b4abddd7 100755
--- a/tests/runTests_DASolidDisplacementFoam.py
+++ b/tests/runTests_DASolidDisplacementFoam.py
@@ -122,4 +122,4 @@
     funcsSens, fail = optFuncs.calcObjFuncSens(xDV, funcs)
     if gcomm.rank == 0:
         reg_write_dict(funcs, 1e-8, 1e-10)
-        reg_write_dict(funcsSens, 1e-6, 1e-8)
+        reg_write_dict(funcsSens, 1e-5, 1e-7)
diff --git a/tests/runTests_DATurboFoamSubsonic.py b/tests/runTests_DATurboFoamSubsonic.py
index 1d25147e..5abbab47 100755
--- a/tests/runTests_DATurboFoamSubsonic.py
+++ b/tests/runTests_DATurboFoamSubsonic.py
@@ -147,6 +147,6 @@
     funcsSens, fail = optFuncs.calcObjFuncSens(xDV, funcs)
     if gcomm.rank == 0:
         reg_write_dict(funcs, 1e-8, 1e-10)
-        reg_write_dict(funcsSens, 1e-6, 1e-8)
+        reg_write_dict(funcsSens, 1e-5, 1e-7)
 
 
diff --git a/tests/runTests_DATurboFoamTransonic.py b/tests/runTests_DATurboFoamTransonic.py
index 8582174c..13662bd2 100755
--- a/tests/runTests_DATurboFoamTransonic.py
+++ b/tests/runTests_DATurboFoamTransonic.py
@@ -161,4 +161,4 @@
     funcsSens, fail = optFuncs.calcObjFuncSens(xDV, funcs)
     if gcomm.rank == 0:
         reg_write_dict(funcs, 1e-8, 1e-10)
-        reg_write_dict(funcsSens, 1e-6, 1e-8)
+        reg_write_dict(funcsSens, 1e-5, 1e-7)