old : CellCenterData2d object The CellCenterData2d object we wish to copy
- Note
- ----
- It may be that this whole thing can be replaced with a copy.deepcopy()
-
"""ifnotisinstance(old,CellCenterData2d):
diff --git a/_modules/pyro/mesh/reconstruction.html b/_modules/pyro/mesh/reconstruction.html
index 364a97295..0388070ec 100644
--- a/_modules/pyro/mesh/reconstruction.html
+++ b/_modules/pyro/mesh/reconstruction.html
@@ -7,7 +7,7 @@
- pyro.mesh.reconstruction — pyro 4.3.0.post6+g075ce404 documentation
+ pyro.mesh.reconstruction — pyro 4.3.0.post7+g903285ee documentation
@@ -38,7 +38,7 @@
-
+
@@ -187,14 +187,13 @@
diff --git a/_sources/advection_basics.rst b/_sources/advection_basics.rst
index 2f467d038..c51cf8067 100644
--- a/_sources/advection_basics.rst
+++ b/_sources/advection_basics.rst
@@ -1,5 +1,6 @@
-Advection solvers
-=================
+*********
+Advection
+*********
The linear advection equation:
@@ -14,7 +15,7 @@ pyro has several solvers for linear advection, which solve the equation
with different spatial and temporal integration schemes.
``advection`` solver
---------------------
+====================
:py:mod:`pyro.advection` implements the directionally unsplit corner
transport upwind algorithm :cite:`colella:1990` with piecewise linear reconstruction.
@@ -29,9 +30,10 @@ The parameters for this solver are:
.. include:: advection_defaults.inc
+.. include:: advection_problems.inc
``advection_fv4`` solver
-------------------------
+========================
:py:mod:`pyro.advection_fv4` uses a fourth-order accurate finite-volume
method with RK4 time integration, following the ideas in
@@ -50,8 +52,10 @@ The parameters for this solver are:
.. include:: advection_fv4_defaults.inc
+.. include:: advection_fv4_problems.inc
+
``advection_nonuniform`` solver
--------------------------------
+===============================
:py:mod:`pyro.advection_nonuniform` models advection with a non-uniform
velocity field. This is used to implement the slotted disk problem
@@ -62,8 +66,11 @@ The parameters for this solver are:
.. include:: advection_nonuniform_defaults.inc
+.. include:: advection_nonuniform_problems.inc
+
+
``advection_rk`` solver
------------------------
+=======================
:py:mod:`pyro.advection_rk` uses a method of lines time-integration
approach with piecewise linear spatial reconstruction for linear
@@ -76,8 +83,10 @@ The parameter for this solver are:
.. include:: advection_rk_defaults.inc
+.. include:: advection_rk_problems.inc
+
``advection_weno`` solver
--------------------------
+=========================
:py:mod:`pyro.advection_weno` uses a WENO reconstruction and method of
lines time-integration
@@ -87,9 +96,11 @@ The main parameters that affect this solver are:
.. include:: advection_weno_defaults.inc
+.. include:: advection_weno_problems.inc
+
General ideas
--------------
+=============
The main use for the advection solver is to understand how Godunov
techniques work for hyperbolic problems. These same ideas will be used
@@ -108,10 +119,10 @@ reconstruction, evolution, and averaging steps:
Examples
---------
+========
smooth
-^^^^^^
+------
The smooth problem initializes a Gaussian profile and advects it with
:math:`u = v = 1` through periodic boundaries for a period. The result is that
@@ -147,22 +158,15 @@ with the ``advection_fv4`` solver. Departures from perfect scaling
are likely due to the use of limiters.
-tophat
-^^^^^^
-
-The tophat problem initializes a circle in the center of the domain
-with value 1, and 0 outside. This has very steep jumps, and the
-limiters will kick in strongly here.
-
Exercises
----------
+=========
The best way to learn these methods is to play with them yourself. The
exercises below are suggestions for explorations and features to add
to the advection solver.
Explorations
-^^^^^^^^^^^^
+------------
* Test the convergence of the solver for a variety of initial
conditions (tophat hat will differ from the smooth case because of
@@ -175,7 +179,7 @@ Explorations
problem?)
Extensions
-^^^^^^^^^^
+----------
* Implement a dimensionally split version of the advection
algorithm. How does the solution compare between the unsplit and
diff --git a/_sources/burgers_basics.rst b/_sources/burgers_basics.rst
index 9f299d1ea..523ad6a9b 100644
--- a/_sources/burgers_basics.rst
+++ b/_sources/burgers_basics.rst
@@ -1,10 +1,13 @@
+*****************
Burgers' Equation
-==================
+*****************
-Burgers' Equation is a nonlinear hyperbolic equation. It has the same form as the advection equation, except that the quantity being advected is the velocity itself.
+Burgers' Equation is a nonlinear hyperbolic equation. It has the same
+form as the advection equation, except that the quantity being
+advected is the velocity itself.
``Inviscid Burgers``
---------------------------------
+====================
A 2D inviscid Burgers' Equation has the following form:
@@ -29,14 +32,25 @@ The parameters for this solver are:
.. include:: burgers_defaults.inc
+.. include:: burgers_problems.inc
+
+Example
+-------
.. image:: burgers.png
:align: center
-The figure above is generated using ``burgers/problems/test.py``, which is used to test the validity of the solver. Bottom-left of the domain has a higher velocity than the top-right domain. With :math:`u_{i,j}=v_{i,j}`, the wave travels diagonally to the top-right with a constant velocity that is equal to the shock speed. ``burgers/problem/verify.py`` can be used to calculate the wave speed using outputs from ``test.py`` and compare to the theoretical shock speed.
+The figure above is generated using ``burgers/problems/test.py``,
+which is used to test the validity of the solver. Bottom-left of the
+domain has a higher velocity than the top-right domain. With
+:math:`u_{i,j}=v_{i,j}`, the wave travels diagonally to the top-right
+with a constant velocity that is equal to the shock
+speed. ``burgers/problem/verify.py`` can be used to calculate the wave
+speed using outputs from ``test.py`` and compare to the theoretical
+shock speed.
``Viscous Burgers``
---------------------------------
+===================
A 2D viscous Burgers' Equation has the following form:
@@ -60,6 +74,10 @@ The parameters for this solver are:
.. include:: burgers_viscous_defaults.inc
+.. include:: burgers_problems.inc
+
+Example
+-------
.. image:: viscous_burgers.png
:align: center
diff --git a/_sources/compressible_basics.rst b/_sources/compressible_basics.rst
index deb7c1f44..9ceb8259b 100644
--- a/_sources/compressible_basics.rst
+++ b/_sources/compressible_basics.rst
@@ -1,5 +1,6 @@
-Compressible hydrodynamics solvers
-==================================
+**************************
+Compressible hydrodynamics
+**************************
The Euler equations of compressible hydrodynamics take the form:
@@ -27,7 +28,7 @@ direction is allowed.
directory in the solver's directory.
``compressible`` solver
------------------------
+=======================
:py:mod:`pyro.compressible` is based on a directionally unsplit (the corner
transport upwind algorithm) piecewise linear method for the Euler
@@ -38,8 +39,11 @@ The parameters for this solver are:
.. include:: compressible_defaults.inc
+.. include:: compressible_problems.inc
+
+
``compressible_rk`` solver
---------------------------
+==========================
:py:mod:`pyro.compressible_rk` uses a method of lines time-integration
approach with piecewise linear spatial reconstruction for the Euler
@@ -49,8 +53,10 @@ The parameters for this solver are:
.. include:: compressible_rk_defaults.inc
+.. include:: compressible_rk_problems.inc
+
``compressible_fv4`` solver
----------------------------
+===========================
:py:mod:`pyro.compressible_fv4` uses a 4th order accurate method with RK4
time integration, following :cite:`mccorquodalecolella`.
@@ -59,9 +65,10 @@ The parameter for this solver are:
.. include:: compressible_fv4_defaults.inc
+.. include:: compressible_fv4_problems.inc
``compressible_sdc`` solver
----------------------------
+===========================
:py:mod:`pyro.compressible_sdc` uses a 4th order accurate method with
spectral-deferred correction (SDC) for the time integration. This
@@ -72,9 +79,10 @@ The parameters for this solver are:
.. include:: compressible_sdc_defaults.inc
+.. include:: compressible_sdc_problems.inc
Example problems
-----------------
+================
.. note::
@@ -88,7 +96,7 @@ Example problems
Sod
-^^^
+---
The Sod problem is a standard hydrodynamics problem. It is a
one-dimensional shock tube (two states separated by an interface),
@@ -119,7 +127,7 @@ is discussed in the notes above, and can be improved in the PPM method
with contact steepening.
Sedov
-^^^^^
+-----
The Sedov blast wave problem is another standard test with an analytic
solution (Sedov 1959). A lot of energy is point into a point in a
@@ -154,7 +162,7 @@ This shows good agreement with the analytic solution.
quad
-^^^^
+----
The quad problem sets up different states in four regions of the
domain and watches the complex interfaces that develop as shocks
@@ -172,7 +180,7 @@ online by Pawel Artymowicz). It is run as:
rt
-^^
+--
The Rayleigh-Taylor problem puts a dense fluid over a lighter one and
perturbs the interface with a sinusoidal velocity. Hydrostatic
@@ -192,7 +200,7 @@ escape the domain. It is run as:
bubble
-^^^^^^
+------
The bubble problem initializes a hot spot in a stratified domain and
watches it buoyantly rise and roll up. This is run as:
@@ -211,10 +219,10 @@ above that rains down on our atmosphere. Also note the acoustic signal
propagating outward from the bubble (visible in the U and e panels).
Exercises
----------
+=========
Explorations
-^^^^^^^^^^^^
+------------
* Measure the growth rate of the Rayleigh-Taylor instability for
different wavenumbers.
@@ -228,7 +236,7 @@ Explorations
Extensions
-^^^^^^^^^^
+----------
* Limit on the characteristic variables instead of the primitive
variables. What changes do you see? (the notes show how to implement
@@ -246,16 +254,3 @@ Extensions
* Swap the piecewise linear reconstruction for piecewise parabolic
(PPM). The notes and the Miller and Colella paper provide a good basis
for this. Research the Roe Riemann solver and implement it in pyro.
-
-
-Going further
--------------
-
-The compressible algorithm presented here is essentially the
-single-grid hydrodynamics algorithm used in the `Castro code `_—an
-adaptive mesh radiation hydrodynamics code developed at
-CCSE/LBNL. `Castro is freely available for download `_.
-
-A simple, pure Fortran, 1-d compressible hydrodynamics code that does
-piecewise constant, linear, or parabolic (PPM) reconstruction is also
-available. See the `hydro1d `_ page.
diff --git a/_sources/diffusion_basics.rst b/_sources/diffusion_basics.rst
index 77b71d3b6..050800a8f 100644
--- a/_sources/diffusion_basics.rst
+++ b/_sources/diffusion_basics.rst
@@ -1,5 +1,9 @@
+*********
Diffusion
-=========
+*********
+
+``diffusion`` solver
+====================
pyro solves the constant-conductivity diffusion equation:
@@ -16,11 +20,14 @@ multigrid class. The main parameters that affect this solver are:
.. include:: diffusion_defaults.inc
+.. include:: diffusion_problems.inc
+
+
Examples
---------
+========
gaussian
-^^^^^^^^
+--------
The gaussian problem initializes a strongly peaked Gaussian centered
in the domain. The analytic solution for this shows that the profile
@@ -46,14 +53,14 @@ restricted in range to bring out the detail at later times.
Exercises
----------
+=========
The best way to learn these methods is to play with them yourself. The
exercises below are suggestions for explorations and features to add
to the advection solver.
Explorations
-^^^^^^^^^^^^
+------------
* Test the convergence of the solver by varying the resolution and
comparing to the analytic solution.
@@ -64,7 +71,7 @@ Explorations
* Setup some other profiles and experiment with different boundary conditions.
Extensions
-^^^^^^^^^^
+----------
* Switch from Crank-Nicolson (2nd order in time) to backward Euler
(1st order in time) and compare the solution and convergence. This
diff --git a/_sources/incompressible_basics.rst b/_sources/incompressible_basics.rst
index c1ed33c00..053044263 100644
--- a/_sources/incompressible_basics.rst
+++ b/_sources/incompressible_basics.rst
@@ -1,5 +1,13 @@
-Incompressible hydrodynamics solver
-===================================
+****************************
+Incompressible hydrodynamics
+****************************
+
+pyro has two different incompressible solvers: ``incompressible`` is
+inviscid and ``incompressible_viscous`` has viscosity.
+
+
+``incompressible`` solver
+=========================
pyro's incompressible solver solves:
@@ -20,6 +28,8 @@ The main parameters that affect this solver are:
.. include:: incompressible_defaults.inc
+.. include:: incompressible_problems.inc
+
Examples
--------
@@ -82,11 +92,119 @@ The dashed line is second order convergence. We see almost second
order behavior with the limiters enabled and slightly better than
second order with no limiting.
+``incompressible_viscous`` solver
+=================================
+
+pyro's incompressible viscous solver solves:
+
+.. math::
+
+ \frac{\partial U}{\partial t} + U \cdot \nabla U + \nabla p &= \nu \nabla^2 U \\
+ \nabla \cdot U &= 0
+
+This is based on the ``incompressible`` solver, but modifies the
+velocity update step to take viscosity into account, by solving two
+parabolic equations (one for each velocity component) using multigrid.
+
+The main parameters that affect this solver are:
+
+.. include:: incompressible_viscous_defaults.inc
+
+.. include:: incompressible_viscous_problems.inc
+
+Examples
+--------
+
+shear
+^^^^^
+
+The same shear problem as in incompressible solver, here with viscosity
+added.
+
+.. prompt:: bash
+
+ pyro_sim.py incompressible_viscous shear inputs.shear
+
+.. image:: shear_viscous.png
+ :align: center
+
+Compare this with the inviscid result. Notice how the velocities have
+diffused in all directions.
+
+cavity
+^^^^^^
+
+The lid-driven cavity is a well-known benchmark problem for hydro codes
+(see e.g. :cite:t:`ghia1982`, :cite:t:`Kuhlmann2019`). In a unit square box
+with initially static fluid, motion is initiated by a "lid" at the top
+boundary, moving to the right with unit velocity. The basic command is:
+
+.. prompt:: bash
+
+ pyro_sim.py incompressible_viscous cavity inputs.cavity
+
+It is interesting to observe what happens when varying the viscosity, or,
+equivalently the Reynolds number (in this case :math:`\rm{Re}=1/\nu` since
+the characteristic length and velocity scales are 1 by default).
+
+|pic1| |pic2| |pic3|
+
+.. |pic1| image:: cavity_Re100.png
+ :width: 32%
+
+.. |pic2| image:: cavity_Re400.png
+ :width: 32%
+
+.. |pic3| image:: cavity_Re1000.png
+ :width: 32%
+
+These plots were made by allowing the code to run for longer and approach a
+steady-state with the option ``driver.max_steps=1000``, then running
+(e.g. for the Re=100 case):
+
+.. prompt:: bash
+
+ python incompressible_viscous/problems/plot_cavity.py cavity_n64_Re100_0406.h5 -Re 100 -o cavity_Re100.png
+
+convergence
+^^^^^^^^^^^
+
+This is the same test as in the incompressible solver. With viscosity,
+an exponential term is added to the solution. Limiting can again be
+disabled by adding ``incompressible.limiter=0`` to the run command.
+The basic set of tests shown below are run as:
+
+.. prompt:: bash
+
+ pyro_sim.py incompressible_viscous converge inputs.converge.32 vis.dovis=0
+ pyro_sim.py incompressible_viscous converge inputs.converge.64 vis.dovis=0
+ pyro_sim.py incompressible_viscous converge inputs.converge.128 vis.dovis=0
+
+The error is measured by comparing with the analytic solution using
+the routine ``incomp_viscous_converge_error.py`` in ``analysis/``. To
+generate the plot below, run
+
+.. prompt:: bash
+
+ python incompressible_viscous/tests/convergence_errors.py convergence_errors.txt
+
+or ``convergence_errors_no_limiter.txt`` after running with that option. Then:
+
+.. prompt:: bash
+
+ python incompressible_viscous/tests/convergence_plot.py
+
+.. image:: incomp_viscous_converge.png
+ :align: center
+
+The solver is converging but below second-order, unlike the inviscid case. Limiting
+does not seem to make a difference here.
+
Exercises
----------
+=========
Explorations
-^^^^^^^^^^^^
+------------
* Disable the MAC projection and run the converge problem—is the method still 2nd order?
@@ -94,29 +212,20 @@ Explorations
* Experiment with what is projected. Try projecting :math:`U_t` to see if that makes a difference.
+* In the lid-driven cavity problem, when does the solution reach a steady-state?
+
+* :cite:`ghia1982` give benchmark velocities at different Reynolds number for the
+ lid-driven cavity problem (see their Table I). Do we agree with their results?
+
Extensions
-^^^^^^^^^^
+----------
* Switch the final projection from a cell-centered approximate
projection to a nodal projection. This will require writing a new
multigrid solver that operates on nodal data.
-* Add viscosity to the system. This will require doing 2 parabolic
- solves (one for each velocity component). These solves will look
- like the diffusion operation, and will update the provisional
- velocity field.
-
* Switch to a variable density system. This will require adding a mass
continuity equation that is advected and switching the projections
to a variable-coefficient form (since ρ now enters).
-Going further
--------------
-
-The incompressible algorithm presented here is a simplified version of
-the projection methods used in the `Maestro low Mach number
-hydrodynamics code `_. Maestro
-can do variable-density incompressible, anelastic, and low Mach number
-stratified flows in stellar (and terrestrial) environments in close
-hydrostatic equilibrium.
diff --git a/_sources/index.rst b/_sources/index.rst
index 283979fe2..688308baa 100644
--- a/_sources/index.rst
+++ b/_sources/index.rst
@@ -61,7 +61,6 @@ new ideas.
compressible_basics
diffusion_basics
incompressible_basics
- incompressible_viscous_basics
lowmach_basics
swe_basics
particles_basics
diff --git a/_sources/lowmach_basics.rst b/_sources/lowmach_basics.rst
index 2f647feab..70fa5e5b3 100644
--- a/_sources/lowmach_basics.rst
+++ b/_sources/lowmach_basics.rst
@@ -1,5 +1,6 @@
-Low Mach number hydrodynamics solver
-====================================
+*****************************
+Low Mach number hydrodynamics
+*****************************
pyro's low Mach hydrodynamics solver is designed for atmospheric
flows. It captures the effects of stratification on a fluid element by
@@ -14,6 +15,8 @@ governing equations are:
with :math:`\nabla p_0 = \rho_0 g` and :math:`\beta_0 = p_0^{1/\gamma}`.
+``lm_atm`` solver
+=================
As with the incompressible solver, we implement a cell-centered approximate projection method.
@@ -21,17 +24,4 @@ The main parameters that affect this solver are:
.. include:: lm_atm_defaults.inc
-Examples
---------
-
-bubble
-^^^^^^
-
-The bubble problem places a buoyant bubble in a stratified atmosphere
-and watches the development of the roll-up due to shear as it
-rises. This is run as:
-
-.. prompt:: bash
-
- pyro_sim.py lm_atm bubble inputs.bubble
-
+.. include:: lm_atm_problems.inc
diff --git a/_sources/swe_basics.rst b/_sources/swe_basics.rst
index 85537485b..b17c5a97c 100644
--- a/_sources/swe_basics.rst
+++ b/_sources/swe_basics.rst
@@ -1,5 +1,6 @@
-Shallow water solver
-====================
+***************************
+Shallow water hydrodynamics
+***************************
The (augmented) shallow water equations take the form:
@@ -13,26 +14,32 @@ with :math:`h` is the fluid height, :math:`U` the fluid velocity, :math:`g` the
gravitational acceleration and :math:`\psi = \psi(x, t)` represents some
passive scalar.
+``swe`` solver
+==============
-The implementation here has flattening at shocks and a choice of Riemann solvers.
+The pyro ``swe`` implementation has flattening at shocks and a choice of Riemann solvers.
The main parameters that affect this solver are:
.. include:: swe_defaults.inc
-Example problems
-----------------
+.. include:: swe_problems.inc
-dam
-^^^
+Examples
+========
-The dam break problem is a standard hydrodynamics problem, analogous to the Sod
-shock tube problem in compressible hydrodynamics. It considers a one-multidimensional
-problem of two regions of fluid at different heights, initially separated by a dam.
-The problem then models the evolution of the system when this dam is removed.
-As for the Sod problem, there exists an exact solution for the dam break problem,
-so we can check our solution against the exact solutions. See Toro's shallow water
-equations book for details on this problem and the exact Riemann solver.
+dam
+---
+
+The dam break problem is a standard hydrodynamics problem, analogous
+to the Sod shock tube problem in compressible hydrodynamics. It
+considers a one-multidimensional problem of two regions of fluid at
+different heights, initially separated by a dam. The problem then
+models the evolution of the system when this dam is removed. As for
+the Sod problem, there exists an exact solution for the dam break
+problem, so we can check our solution against the exact solutions. See
+Toro's shallow water equations book for details on this problem and
+the exact Riemann solver.
Because it is one-dimensional, we run it in narrow domains in the x- or
y-directions. It can be run as:
@@ -57,40 +64,11 @@ slightly better than the HLLC solver, with less smearing at the shock
and head/tail of the rarefaction.
-quad
-^^^^
-
-The quad problem sets up different states in four regions of the
-domain and watches the complex interfaces that develop as shocks
-interact. This problem has appeared in several places (and a `detailed
-investigation
-`_ is
-online by Pawel Artymowicz). It is run as:
-
-.. prompt:: bash
-
- pyro_sim.py swe quad inputs.quad
-
-
-kh
-^^
-
-The Kelvin-Helmholtz problem models three layers of fluid: two at the top and
-bottom of the domain travelling in one direction, one in the central part of the
-domain travelling in the opposite direction. At the interface of the layers,
-shearing produces the characteristic Kelvin-Helmholtz instabilities, just as
-is seen in the standard compressible problem. It is run as:
-
-.. prompt:: bash
-
- pyro_sim.py swe kh inputs.kh
-
-
Exercises
----------
+=========
Explorations
-^^^^^^^^^^^^
+------------
* There are multiple Riemann solvers in the swe
algorithm. Run the same problem with the different Riemann solvers
@@ -101,7 +79,7 @@ Explorations
Extensions
-^^^^^^^^^^
+----------
* Limit on the characteristic variables instead of the primitive
variables. What changes do you see? (the notes show how to implement
diff --git a/_static/documentation_options.js b/_static/documentation_options.js
index 328ba42db..af35c0f7f 100644
--- a/_static/documentation_options.js
+++ b/_static/documentation_options.js
@@ -1,5 +1,5 @@
const DOCUMENTATION_OPTIONS = {
- VERSION: '4.3.0.post6+g075ce404',
+ VERSION: '4.3.0.post7+g903285ee',
LANGUAGE: 'en',
COLLAPSE_INDEX: false,
BUILDER: 'html',
diff --git a/ack.html b/ack.html
index 363eb5f12..93f14640d 100644
--- a/ack.html
+++ b/ack.html
@@ -8,7 +8,7 @@
- Acknowledgments — pyro 4.3.0.post6+g075ce404 documentation
+ Acknowledgments — pyro 4.3.0.post7+g903285ee documentation
@@ -39,7 +39,7 @@
-
+
@@ -188,14 +188,13 @@
The smooth problem initializes a Gaussian profile and advects it with
\(u = v = 1\) through periodic boundaries for a period. The result is that
the final state should be identical to the initial state—any
@@ -935,12 +1007,6 @@
smooth#advection_fv4 solver. Departures from perfect scaling
are likely due to the use of limiters.
The tophat problem initializes a circle in the center of the domain
-with value 1, and 0 outside. This has very steep jumps, and the
-limiters will kick in strongly here.
Burgers’ Equation is a nonlinear hyperbolic equation. It has the same form as the advection equation, except that the quantity being advected is the velocity itself.
+
Burgers’ Equation is a nonlinear hyperbolic equation. It has the same
+form as the advection equation, except that the quantity being
+advected is the velocity itself.
The figure above is generated using burgers/problems/test.py, which is used to test the validity of the solver. Bottom-left of the domain has a higher velocity than the top-right domain. With \(u_{i,j}=v_{i,j}\), the wave travels diagonally to the top-right with a constant velocity that is equal to the shock speed. burgers/problem/verify.py can be used to calculate the wave speed using outputs from test.py and compare to the theoretical shock speed.
+
The figure above is generated using burgers/problems/test.py,
+which is used to test the validity of the solver. Bottom-left of the
+domain has a higher velocity than the top-right domain. With
+\(u_{i,j}=v_{i,j}\), the wave travels diagonally to the top-right
+with a constant velocity that is equal to the shock
+speed. burgers/problem/verify.py can be used to calculate the wave
+speed using outputs from test.py and compare to the theoretical
+shock speed.
The figure above is generated using
burgers_viscous/problems/test.py, which has the identical setup as
in burgers/problems/test.py. With diffusion added to the system,
we see the shock (discontinuity) is smeared out as system evolves.
A RT problem with two distinct modes: short wave length on the
+left and long wavelength on the right. This allows one to see
+how the growth rate depends on wavenumber.
The Sod problem is a standard hydrodynamics problem. It is a
one-dimensional shock tube (two states separated by an interface),
that exhibits all three hydrodynamic waves: a shock, contact, and
@@ -1014,8 +1416,8 @@
The Sedov blast wave problem is another standard test with an analytic
solution (Sedov 1959). A lot of energy is point into a point in a
uniform medium and a blast wave propagates outward. The Sedov problem
@@ -1035,8 +1437,8 @@
The quad problem sets up different states in four regions of the
domain and watches the complex interfaces that develop as shocks
interact. This problem has appeared in several places (and a detailed
@@ -1045,8 +1447,8 @@
The Rayleigh-Taylor problem puts a dense fluid over a lighter one and
perturbs the interface with a sinusoidal velocity. Hydrostatic
boundary conditions are used to ensure any initial pressure waves can
@@ -1055,8 +1457,8 @@
The compressible algorithm presented here is essentially the
-single-grid hydrodynamics algorithm used in the Castro code—an
-adaptive mesh radiation hydrodynamics code developed at
-CCSE/LBNL. Castro is freely available for download.
-
A simple, pure Fortran, 1-d compressible hydrodynamics code that does
-piecewise constant, linear, or parabolic (PPM) reconstruction is also
-available. See the hydro1d page.
-
