From 45024fa0122c962c1ad00268d14a511571d2c61a Mon Sep 17 00:00:00 2001
From: rubenzorrilla <rubenzorrillamartinez@hotmail.com>
Date: Wed, 7 Aug 2024 10:18:43 +0200
Subject: [PATCH 1/2] Upload case files

---
 .../embedded_fsi_membrane_airfoil/README.md   |     34 +
 .../source/FluidMaterials.json                |     20 +
 .../source/MainKratos.py                      |     46 +
 .../source/ProjectParameters.json             |    276 +
 .../source/StructuralMaterials.json           |     15 +
 .../embedded_fsi_membrane_airfoil_fluid.mdpa  | 434113 +++++++++++++++
 ...bedded_fsi_membrane_airfoil_structure.mdpa |    933 +
 7 files changed, 435437 insertions(+)
 create mode 100644 fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/README.md
 create mode 100644 fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/FluidMaterials.json
 create mode 100755 fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/MainKratos.py
 create mode 100644 fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/ProjectParameters.json
 create mode 100644 fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/StructuralMaterials.json
 create mode 100644 fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/embedded_fsi_membrane_airfoil_fluid.mdpa
 create mode 100644 fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/embedded_fsi_membrane_airfoil_structure.mdpa

diff --git a/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/README.md b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/README.md
new file mode 100644
index 00000000..1f677c3d
--- /dev/null
+++ b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/README.md
@@ -0,0 +1,34 @@
+# Mixer with flexible blades
+
+**Author:** [Rubén Zorrilla](https://github.com/rubenzorrilla)
+
+**Kratos version:** 9.1
+
+**Source files:** [Mixer with flexible blades](https://github.com/KratosMultiphysics/Examples/tree/master/fluid_structure_interaction/validation/embedded_fsi_mixer_Y/source)
+
+## Case Specification
+This example is specifically conceived to prove the extended scope of applicatoin of embedded mesh methods. Hence, it involves extremely large rotations, which would be impossible to solve by using a body fitted ALE based approach.
+
+The problem is set up as a 2D idealization of a turbine mixer with clockwise-anticlockwise alternate rotation. The problem geometry is a unit diameter circle with three embedded flexible blades. An imposed rotation is enforced in the blades axis to emulate the spin of the rotor. Such rotation changes the direction (anticlockwise to clockwise and viceversa) after More details on the dimensions, material settings and boundary conditions can be found in [here](https://doi.org/10.1016/j.cma.2020.113179).
+
+## Results
+The fluid domain is meshed with a 45 and 540 radial and perimeter subdivisions Q1P1 elements centered structured mesh. Each one of the flexible blades is meshed with an 8x39 subdivisions structured mesh made with Total Lagrangian quadrilateral elements. The problem is run for 20s so three complete rotations (anticlockwise - clockwise - anticlockwise) are simulated.
+
+The obtained velocity and pressure fields, together with the level set zero isosurface representing the deformed geometry, are shown below.
+
+<p align="center">
+<figure>
+  <img src="data/embedded_fsi_mixer_Y_v.gif" alt="Velocity field and level set isosurface." style="width: 600px;"/>
+  <figcaption>Velocity field and level set isosurface.</figcaption>
+</figure>
+</p>
+
+<p align="center">
+<figure>
+  <img src="data/embedded_fsi_mixer_Y_p.gif" alt="Pressure field and level set isosurface." style="width: 600px;"/>
+  <figcaption>Pressure field and level set isosurface.</figcaption>
+</figure>
+</p>
+
+## References
+R. Zorrilla, R. Rossi, R. Wüchner and E. Oñate, An embedded Finite Element framework for the resolution of strongly coupled Fluid–Structure Interaction problems. Application to volumetric and membrane-like structures, Computer Methods in Applied Mechanics and Engineering (368), [10.1016/j.cma.2020.113179](https://doi.org/10.1016/j.cma.2020.113179)
diff --git a/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/FluidMaterials.json b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/FluidMaterials.json
new file mode 100644
index 00000000..9c71f628
--- /dev/null
+++ b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/FluidMaterials.json
@@ -0,0 +1,20 @@
+{
+    "properties" : [{
+        "model_part_name" : "FluidModelPart",
+        "properties_id"   : 0,
+        "Material"        : null
+    },{
+        "model_part_name" : "FluidModelPart.FluidParts_Fluid",
+        "properties_id"   : 1,
+        "Material"        : {
+            "constitutive_law" : {
+                "name" : "Newtonian2DLaw"
+            },
+            "Variables"        : {
+                "DENSITY"           : 1.0,
+                "DYNAMIC_VISCOSITY" : 0.000155
+            },
+            "Tables"           : null
+        }
+    }]
+}
diff --git a/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/MainKratos.py b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/MainKratos.py
new file mode 100755
index 00000000..3475e0fa
--- /dev/null
+++ b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/MainKratos.py
@@ -0,0 +1,46 @@
+import sys
+import math
+import time
+import importlib
+
+import KratosMultiphysics
+
+def CreateAnalysisStageWithFlushInstance(cls, global_model, parameters):
+    class AnalysisStageWithFlush(cls):
+
+        def __init__(self, model,project_parameters, flush_frequency=10.0):
+            super().__init__(model,project_parameters)
+            self.flush_frequency = flush_frequency
+            self.last_flush = time.time()
+            sys.stdout.flush()
+
+        def Initialize(self):
+            super().Initialize()
+            sys.stdout.flush()
+
+        def FinalizeSolutionStep(self):
+            super().FinalizeSolutionStep()
+
+            if self.parallel_type == "OpenMP":
+                now = time.time()
+                if now - self.last_flush > self.flush_frequency:
+                    sys.stdout.flush()
+                    self.last_flush = now
+
+    return AnalysisStageWithFlush(global_model, parameters)
+
+if __name__ == "__main__":
+
+    with open("ProjectParameters.json", 'r') as parameter_file:
+        parameters = KratosMultiphysics.Parameters(parameter_file.read())
+
+    analysis_stage_module_name = parameters["analysis_stage"].GetString()
+    analysis_stage_class_name = analysis_stage_module_name.split('.')[-1]
+    analysis_stage_class_name = ''.join(x.title() for x in analysis_stage_class_name.split('_'))
+
+    analysis_stage_module = importlib.import_module(analysis_stage_module_name)
+    analysis_stage_class = getattr(analysis_stage_module, analysis_stage_class_name)
+
+    global_model = KratosMultiphysics.Model()
+    simulation = CreateAnalysisStageWithFlushInstance(analysis_stage_class, global_model, parameters)
+    simulation.Run()
diff --git a/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/ProjectParameters.json b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/ProjectParameters.json
new file mode 100644
index 00000000..84bd6e86
--- /dev/null
+++ b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/ProjectParameters.json
@@ -0,0 +1,276 @@
+ {
+    "analysis_stage" : "KratosMultiphysics.FSIApplication.fsi_analysis",
+    "problem_data": {
+        "problem_name": "embedded_fsi_membrane_airfoil",
+        "parallel_type": "OpenMP",
+        "echo_level": 0,
+        "start_time": 0.0,
+        "end_time": 1.0e0
+    },
+    "solver_settings": {
+        "solver_type": "partitioned_embedded",
+        "coupling_scheme": "dirichlet_neumann",
+        "echo_level": 1,
+        "structure_solver_settings": {
+            "solver_type"                        : "Dynamic",
+            "model_part_name"                    : "Structure",
+            "domain_size"                        : 2,
+            "echo_level"                         : 0,
+            "analysis_type"                      : "non_linear",
+            "time_integration_method"            : "implicit",
+            "scheme_type"                        : "bossak",
+            "model_import_settings"              : {
+                "input_type": "mdpa",
+                "input_filename": "embedded_fsi_membrane_airfoil_structure"
+            },
+            "material_import_settings": {
+                "materials_filename": "StructuralMaterials.json"
+            },
+            "time_stepping": {
+                "time_step": 5e-3
+            },
+            "line_search"                        : false,
+            "convergence_criterion"              : "residual_criterion",
+            "displacement_relative_tolerance"    : 1e-5,
+            "displacement_absolute_tolerance"    : 1e-7,
+            "residual_relative_tolerance"        : 1e-5,
+            "residual_absolute_tolerance"        : 1e-7,
+            "max_iteration"                      : 20
+        },
+        "fluid_solver_settings":{
+            "model_part_name"             : "FluidModelPart",
+            "domain_size"                 : 2,
+            "solver_type"                 : "Embedded",
+            "model_import_settings"       : {
+                "input_type"     : "mdpa",
+                "input_filename" : "embedded_fsi_membrane_airfoil_fluid"
+            },
+            "material_import_settings": {
+                "materials_filename": "FluidMaterials.json"
+            },
+            "distance_modification_settings": {
+                "distance_threshold": 1.0e-3
+            },
+            "echo_level"                  : 0,
+            "compute_reactions"           : true,
+            "maximum_iterations"          : 10,
+            "relative_velocity_tolerance" : 1e-5,
+            "absolute_velocity_tolerance" : 1e-7,
+            "relative_pressure_tolerance" : 1e-5,
+            "absolute_pressure_tolerance" : 1e-7,
+            "assign_neighbour_elements_to_conditions" : true,
+            "volume_model_part_name"      : "FluidModelPart.FluidParts_Fluid",
+            "skin_parts"                  : ["FluidModelPart.AutomaticInlet2D_Inlet","FluidModelPart.Outlet2D_Outlet","FluidModelPart.VelocityConstraints2D_Walls"],
+            "no_skin_parts"               : [],
+            "time_stepping"               : {
+                "automatic_time_step": false,
+                "time_step": 5e-3
+            },
+            "formulation": {
+                "element_type": "embedded_weakly_compressible_navier_stokes_discontinuous",
+                "is_slip": true,
+                "slip_length": 1.0e6,
+                "penalty_coefficient": 1.0e3,
+                "dynamic_tau": 1.0
+            },
+            "fm_ale_settings": {
+                "fm_ale_step_frequency": 1,
+                "mesh_movement": "implicit",
+                "fm_ale_solver_settings": {
+                    "structure_model_part_name": "FSICouplingInterfaceFluid",
+                    "virtual_model_part_name": "VirtualModelPart",
+                    "linear_solver_settings": {
+                        "preconditioner_type": "amg",
+                        "solver_type": "amgcl",
+                        "smoother_type": "ilu0",
+                        "krylov_type": "cg",
+                        "max_iteration": 2000,
+                        "verbosity": 0,
+                        "tolerance": 1e-8,
+                        "scaling": false,
+                        "use_block_matrices_if_possible": true
+                    },
+                    "embedded_nodal_variable_settings": {
+                        "gradient_penalty_coefficient": 5.0e-2,
+                        "linear_solver_settings": {
+                            "preconditioner_type": "amg",
+                            "solver_type": "amgcl",
+                            "smoother_type": "ilu0",
+                            "krylov_type": "cg",
+                            "max_iteration": 2000,
+                            "verbosity": 0,
+                            "tolerance": 1e-8,
+                            "scaling": false,
+                            "block_size": 1,
+                            "use_block_matrices_if_possible": true
+                        }
+                    }
+                }
+            }
+        },
+        "coupling_settings":{
+            "nl_tol": 1e-4,
+            "nl_max_it": 10,
+            "coupling_strategy_settings": {
+                "solver_type": "MVQN",
+                "w_0": 0.5,
+                "abs_cut_off_tol" : 1e-6
+            },
+            "structure_interfaces_list": ["Structure.LinePressure2D_Load"]
+        }
+	},
+    "processes":{
+        "structure_constraints_process_list" : [{
+            "python_module" : "assign_vector_variable_process",
+            "kratos_module" : "KratosMultiphysics",
+            "process_name"  : "AssignVectorVariableProcess",
+            "Parameters"    : {
+                "model_part_name" : "Structure.DISPLACEMENT_EndPoints",
+                "variable_name"   : "DISPLACEMENT",
+                "interval"        : [0.0,"End"],
+                "constrained"     : [true,true,true],
+                "value"           : [0.0,0.0,0.0]
+            }
+        }],
+        "structure_loads_process_list"       : [],
+        "fluid_initial_conditions_process_list"  : [],
+        "fluid_boundary_conditions_process_list" : [{
+            "python_module" : "apply_inlet_process",
+            "kratos_module" : "KratosMultiphysics.FluidDynamicsApplication",
+            "process_name"  : "ApplyInletProcess",
+            "Parameters"    : {
+                "model_part_name" : "FluidModelPart.AutomaticInlet2D_Inlet",
+                "variable_name"   : "VELOCITY",
+                "interval"        : [0.0,"End"],
+                "modulus"         : 2.5833,
+                "direction"       : "automatic_inwards_normal"
+            }
+        },{
+            "python_module" : "apply_outlet_process",
+            "kratos_module" : "KratosMultiphysics.FluidDynamicsApplication",
+            "process_name"  : "ApplyOutletProcess",
+            "Parameters"    : {
+                "model_part_name"    : "FluidModelPart.Outlet2D_Outlet",
+                "variable_name"      : "PRESSURE",
+                "constrained"        : true,
+                "value"              : 0.0,
+                "hydrostatic_outlet" : false,
+                "h_top"              : 0.0
+            }
+        },{
+            "python_module" : "assign_vector_variable_process",
+            "kratos_module" : "KratosMultiphysics",
+            "process_name"  : "AssignVectorVariableProcess",
+            "Parameters"    : {
+                "model_part_name" : "FluidModelPart.VelocityConstraints2D_Walls",
+                "variable_name"   : "VELOCITY",
+                "interval"        : [0.0,"End"],
+                "constrained"     : [false,true,false],
+                "value"           : [null,0.0,null]
+            }
+        },{
+            "python_module" : "assign_vector_variable_process",
+            "kratos_module" : "KratosMultiphysics",
+            "process_name"  : "AssignVectorVariableProcess",
+            "Parameters"    : {
+                "model_part_name" : "FluidModelPart.AutomaticInlet2D_Inlet",
+                "variable_name"   : "MESH_DISPLACEMENT",
+                "interval"        : [0.0,"End"],
+                "constrained"     : [true,true,false],
+                "value"           : [0.0,0.0,null]
+            }
+        },{
+            "python_module" : "assign_vector_variable_process",
+            "kratos_module" : "KratosMultiphysics",
+            "process_name"  : "AssignVectorVariableProcess",
+            "Parameters"    : {
+                "model_part_name" : "FluidModelPart.Outlet2D_Outlet",
+                "variable_name"   : "MESH_DISPLACEMENT",
+                "interval"        : [0.0,"End"],
+                "constrained"     : [true,true,false],
+                "value"           : [0.0,0.0,null]
+            }
+        },{
+            "python_module" : "assign_vector_variable_process",
+            "kratos_module" : "KratosMultiphysics",
+            "process_name"  : "AssignVectorVariableProcess",
+            "Parameters"    : {
+                "model_part_name" : "FluidModelPart.VelocityConstraints2D_Walls",
+                "variable_name"   : "MESH_DISPLACEMENT",
+                "interval"        : [0.0,"End"],
+                "constrained"     : [true,true,false],
+                "value"           : [0.0,0.0,null]
+            }
+        }],
+        "fluid_gravity" : [],
+        "fluid_auxiliar_process_list" : [{
+            "python_module": "apply_embedded_postprocess_process",
+            "kratos_module": "KratosMultiphysics.FluidDynamicsApplication",
+            "process_name": "ApplyEmbeddedPostprocessrocess",
+            "Parameters": {
+                "model_part_name": "FluidModelPart.FluidParts_Fluid"
+            }
+        }]
+    },
+    "output_processes":{
+        "gid_output" : [{
+            "python_module" : "gid_output_process",
+            "kratos_module" : "KratosMultiphysics",
+            "process_name"  : "GiDOutputProcess",
+            "Parameters"    : {
+                "model_part_name"        : "Structure",
+                "output_name"            : "gordnier_membrane_structure",
+                "postprocess_parameters" : {
+                    "result_file_configuration" : {
+                        "gidpost_flags"       : {
+                            "GiDPostMode"           : "GiD_PostBinary",
+                            "WriteDeformedMeshFlag" : "WriteDeformed",
+                            "WriteConditionsFlag"   : "WriteConditions",
+                            "MultiFileFlag"         : "SingleFile"
+                        },
+                        "file_label"          : "time",
+                        "output_control_type" : "step",
+                        "output_interval"     : 1,
+                        "body_output"         : true,
+                        "node_output"         : false,
+                        "skin_output"         : false,
+                        "plane_output"        : [],
+                        "nodal_results"       : ["DISPLACEMENT","VELOCITY","ACCELERATION","REACTION","LINE_LOAD"],
+                        "gauss_point_results" : []
+                    },
+                    "point_data_configuration"  : []
+                }
+            }
+        },{
+            "python_module": "gid_output_process",
+            "kratos_module": "KratosMultiphysics",
+            "process_name": "GiDOutputProcess",
+            "Parameters": {
+                "model_part_name": "FluidModelPart.FluidParts_Fluid",
+                "output_name": "gordnier_membrane_fluid",
+                "postprocess_parameters": {
+                    "result_file_configuration": {
+                        "gidpost_flags": {
+                            "GiDPostMode": "GiD_PostBinary",
+                            "WriteDeformedMeshFlag": "WriteDeformed",
+                            "WriteConditionsFlag": "WriteConditions",
+                            "MultiFileFlag": "SingleFile"
+                        },
+                        "file_label": "time",
+                        "output_control_type": "step",
+                        "output_interval" : 1,
+                        "body_output": true,
+                        "node_output": false,
+                        "skin_output": false,
+                        "plane_output": [],
+                        "nodal_results": ["VELOCITY","PRESSURE","MESH_VELOCITY"],
+                        "nodal_nonhistorical_results": [],
+                        "elemental_conditional_flags_results": [],
+                        "gauss_point_results": []
+                    },
+                    "point_data_configuration": []
+                }
+            }
+        }]
+    }
+}
diff --git a/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/StructuralMaterials.json b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/StructuralMaterials.json
new file mode 100644
index 00000000..b78a6b5b
--- /dev/null
+++ b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/StructuralMaterials.json
@@ -0,0 +1,15 @@
+{
+    "properties" : [{
+        "model_part_name" : "Structure.Parts_Cable_Membrane",
+        "properties_id"   : 1,
+        "Material"        : {
+            "Variables"        : {
+                "DENSITY"             : 441.75,
+                "YOUNG_MODULUS"       : 250000.0,
+                "THICKNESS"           : 0.0002,
+                "PRESTRESS_VECTOR"    : [0.0]
+            },
+            "Tables"           : null
+        }
+    }]
+}
diff --git a/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/embedded_fsi_membrane_airfoil_fluid.mdpa b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/embedded_fsi_membrane_airfoil_fluid.mdpa
new file mode 100644
index 00000000..902395de
--- /dev/null
+++ b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/embedded_fsi_membrane_airfoil_fluid.mdpa
@@ -0,0 +1,434113 @@
+Begin ModelPartData
+//  VARIABLE_NAME value
+End ModelPartData
+
+Begin Properties 0
+End Properties
+
+Begin Nodes
+    1   2.4000000000  -1.2000000000   0.0000000000
+    2   2.3750000000  -1.2000000000   0.0000000000
+    3   2.4000000000  -1.1750000000   0.0000000000
+    4   2.3792666667  -1.1720599802   0.0000000000
+    5   2.3552777778  -1.1789387716   0.0000000000
+    6   2.3500000000  -1.2000000000   0.0000000000
+    7   2.4000000000  -1.1500000000   0.0000000000
+    8   2.3660555556  -1.1563611294   0.0000000000
+    9   2.3761277778  -1.1375289364   0.0000000000
+   10   2.3300462963  -1.1800578470   0.0000000000
+   11   2.3375000001  -1.1599192252   0.0000000000
+   12   2.3250000000  -1.2000000000   0.0000000000
+   13   2.4000000000  -1.1250000000   0.0000000000
+   14   2.3500000001  -1.1382685901   0.0000000000
+   15   2.3645833334  -1.1180149625   0.0000000000
+   16   2.3098688272  -1.1587726409   0.0000000000
+   17   2.3000000000  -1.2000000000   0.0000000000
+   18   2.4000000000  -1.1000000000   0.0000000000
+   19   2.3211319016  -1.1371808805   0.0000000000
+   20   2.3000000001  -1.1815698603   0.0000000000
+   21   2.3375000001  -1.1166179550   0.0000000000
+   22   2.3750000001  -1.0949673199   0.0000000000
+   23   2.3500000001  -1.0949673199   0.0000000000
+   24   2.2750000000  -1.2000000000   0.0000000000
+   25   2.4000000000  -1.0750000000   0.0000000000
+   26   2.2919225823  -1.1361094122   0.0000000000
+   27   2.3063424140  -1.1150033086   0.0000000000
+   28   2.2791666667  -1.1577722283   0.0000000000
+   29   2.3250000001  -1.0949673199   0.0000000000
+   30   2.3625000001  -1.0733166848   0.0000000000
+   31   2.2625000000  -1.1783493649   0.0000000000
+   32   2.3375000001  -1.0733166848   0.0000000000
+   33   2.2500000000  -1.2000000000   0.0000000000
+   34   2.4000000000  -1.0500000000   0.0000000000
+   35   2.3750000001  -1.0516660497   0.0000000000
+   36   2.2750000000  -1.1133974596   0.0000000000
+   37   2.2625000000  -1.1350480947   0.0000000000
+   38   2.3125000001  -1.0733166848   0.0000000000
+   39   2.2500000000  -1.1566987298   0.0000000000
+   40   2.2875000000  -1.0917468245   0.0000000000
+   41   2.3500000001  -1.0516660497   0.0000000000
+   42   2.2375000000  -1.1783493649   0.0000000000
+   43   2.3250000001  -1.0516660497   0.0000000000
+   44   2.2500000000  -1.1133974596   0.0000000000
+   45   2.3645833334  -1.0291795122   0.0000000000
+   46   2.2250000000  -1.2000000000   0.0000000000
+   47   2.2625000000  -1.0917468245   0.0000000000
+   48   2.4000000000  -1.0250000000   0.0000000000
+   49   2.2375000000  -1.1350480947   0.0000000000
+   50   2.3000000001  -1.0516660497   0.0000000000
+   51   2.2250000000  -1.1566987298   0.0000000000
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+End Nodes
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+    Begin SubModelPartNodes
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+End SubModelPart
+Begin SubModelPart Outlet2D_Outlet // Group Outlet // Subtree Outlet2D
+    Begin SubModelPartNodes
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+    Begin SubModelPartElements
+    End SubModelPartElements
+    Begin SubModelPartConditions
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+    End SubModelPartConditions
+End SubModelPart
+Begin SubModelPart VelocityConstraints2D_Walls // Group Walls // Subtree VelocityConstraints2D
+    Begin SubModelPartNodes
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+    End SubModelPartNodes
+End SubModelPart
diff --git a/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/embedded_fsi_membrane_airfoil_structure.mdpa b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/embedded_fsi_membrane_airfoil_structure.mdpa
new file mode 100644
index 00000000..e54eefaf
--- /dev/null
+++ b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/embedded_fsi_membrane_airfoil_structure.mdpa
@@ -0,0 +1,933 @@
+Begin ModelPartData
+//  VARIABLE_NAME value
+End ModelPartData
+
+Begin Properties 0
+End Properties
+Begin Nodes
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+
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+End SubModelPart
+Begin SubModelPart DISPLACEMENT_EndPoints // Group EndPoints // Subtree DISPLACEMENT
+    Begin SubModelPartNodes
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+    End SubModelPartNodes
+End SubModelPart
+Begin SubModelPart LinePressure2D_Load // Group Load // Subtree LinePressure2D
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+    End SubModelPartConditions
+End SubModelPart

From 9f9ac593ad87cf6245d556a69058d9b515fc5767 Mon Sep 17 00:00:00 2001
From: rubenzorrilla <rubenzorrillamartinez@hotmail.com>
Date: Thu, 8 Aug 2024 18:33:09 +0200
Subject: [PATCH 2/2] Fine

---
 fluid_structure_interaction/README.md         |      1 +
 .../embedded_fsi_membrane_airfoil/README.md   |     45 +
 .../embedded_fsi_membrane_airfoil_fluid_p.gif |    Bin 0 -> 5567782 bytes
 .../embedded_fsi_membrane_airfoil_fluid_v.gif |    Bin 0 -> 6642842 bytes
 ...edded_fsi_membrane_airfoil_structure_u.gif |    Bin 0 -> 3480255 bytes
 .../source/FluidMaterials.json                |     20 +
 .../source/MainKratos.py                      |     46 +
 .../source/ProjectParameters.json             |    282 +
 .../source/StructuralMaterials.json           |     15 +
 .../embedded_fsi_membrane_airfoil_fluid.mdpa  | 434113 +++++++++++++++
 ...bedded_fsi_membrane_airfoil_structure.mdpa |    933 +
 .../validation/embedded_fsi_mixer_Y/README.md |      2 +-
 12 files changed, 435456 insertions(+), 1 deletion(-)
 create mode 100644 fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/README.md
 create mode 100644 fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/data/embedded_fsi_membrane_airfoil_fluid_p.gif
 create mode 100644 fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/data/embedded_fsi_membrane_airfoil_fluid_v.gif
 create mode 100644 fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/data/embedded_fsi_membrane_airfoil_structure_u.gif
 create mode 100644 fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/FluidMaterials.json
 create mode 100755 fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/MainKratos.py
 create mode 100644 fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/ProjectParameters.json
 create mode 100644 fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/StructuralMaterials.json
 create mode 100644 fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/embedded_fsi_membrane_airfoil_fluid.mdpa
 create mode 100644 fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/embedded_fsi_membrane_airfoil_structure.mdpa

diff --git a/fluid_structure_interaction/README.md b/fluid_structure_interaction/README.md
index ebe62d9c..ad03b2ed 100644
--- a/fluid_structure_interaction/README.md
+++ b/fluid_structure_interaction/README.md
@@ -5,6 +5,7 @@ Coming soon...
 
 ## Validation Cases
 - [FSI lid driven cavity](https://github.com/KratosMultiphysics/Examples/blob/master/fluid_structure_interaction/validation/fsi_lid_driven_cavity/README.md)
+- [Flexible membrane airfoil (embedded)](https://github.com/KratosMultiphysics/Examples/blob/master/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/README.md)
 - [Mixer with flexible blades (embedded)](https://github.com/KratosMultiphysics/Examples/blob/master/fluid_structure_interaction/validation/embedded_fsi_mixer_Y/README.md)
 - [Mok benchmark](https://github.com/KratosMultiphysics/Examples/blob/master/fluid_structure_interaction/validation/fsi_mok/README.md)
 - [Mok benchmark (embedded)](https://github.com/KratosMultiphysics/Examples/blob/master/fluid_structure_interaction/validation/embedded_fsi_mok/README.md)
diff --git a/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/README.md b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/README.md
new file mode 100644
index 00000000..e51a50b1
--- /dev/null
+++ b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/README.md
@@ -0,0 +1,45 @@
+# Flexible membrane airfoil
+
+**Author:** [Rubén Zorrilla](https://github.com/rubenzorrilla)
+
+**Kratos version:** 9.5
+
+**Source files:** [Flexible membrane airfoil](https://github.com/KratosMultiphysics/Examples/tree/master/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source)
+
+## Case Specification
+This example reproduces a reduced-scale experiment of a flexible membrane airfoil[1]. The embedded (i.e., CutFEM) framework for thin-walled bodies is applied in order to avoid the preprocessing and mesh entanglement issues appearing when using volumetric meshes around membrane-like bodies [2].
+
+The problem set up consists in a 2D idealization of the flexible membrane airfoil at an angle of attack of 4º. The lenght and thickness of the membrane are 0.15m and 2e-4m, respectively, while the material parameters are a Young modulus of 250e3Pa and zero Poisson ration. The fluid properties are set such that Re=2500. The structure and fluid density ratio is 441.75. The inlet characteristic velocity is 2.5833m/s.
+
+## Results
+The fluid domain is meshed with a 144k P1P1 elements unstructured mesh. The membrane is meshed with 128 line elements implementing a simplified 2D non-linear membrane formulation. The problem is run with a ramp up function of 1s and for an extra second so to ensure that the membrane reaches the steady state.
+
+The steady state velocity and pressure contour fields as well as the displacement vector field are shown below. The obtained results are in line with similar numerical experiments [3].
+
+<p align="center">
+<figure>
+  <img src="data/embedded_fsi_membrane_airfoil_fluid_v.gif" alt="Fluid velocity contour field." style="width: 600px;"/>
+  <figcaption>Velocity field and level set isosurface.</figcaption>
+</figure>
+</p>
+
+<p align="center">
+<figure>
+  <img src="data/embedded_fsi_membrane_airfoil_fluid_p.gif" alt="Fluid pressure contour field." style="width: 600px;"/>
+  <figcaption>Pressure field and level set isosurface.</figcaption>
+</figure>
+</p>
+
+<p align="center">
+<figure>
+  <img src="data/embedded_fsi_membrane_airfoil_structure_u.gif" alt="Membrane displacement vector field." style="width: 600px;"/>
+  <figcaption>Pressure field and level set isosurface.</figcaption>
+</figure>
+</p>
+
+## References
+[1] P. Rojratsirikul, Z. Wang and I. Gursul, I, Unsteady Aerodynamics of Membrane Airfoils. Paper presented at 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 2008 [10.2514/6.2008-613](https://doi.org/10.2514/6.2008-613).
+
+[2] R. Zorrilla, R. Rossi, R. Wüchner and E. Oñate, An embedded Finite Element framework for the resolution of strongly coupled Fluid–Structure Interaction problems. Application to volumetric and membrane-like structures, Computer Methods in Applied Mechanics and Engineering (368), 2020 [10.1016/j.cma.2020.113179](https://doi.org/10.1016/j.cma.2020.113179).
+
+[3] R. E. Gordnier, High fidelity computational simulation of a membrane wing airfoil, Journal of Fluids and Structures (25), 2009, [10.1016/j.jfluidstructs.2009.03.004](https://doi.org/10.1016/j.jfluidstructs.2009.03.004).
diff --git a/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/data/embedded_fsi_membrane_airfoil_fluid_p.gif b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/data/embedded_fsi_membrane_airfoil_fluid_p.gif
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HcmV?d00001

diff --git a/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/FluidMaterials.json b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/FluidMaterials.json
new file mode 100644
index 00000000..9c71f628
--- /dev/null
+++ b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/FluidMaterials.json
@@ -0,0 +1,20 @@
+{
+    "properties" : [{
+        "model_part_name" : "FluidModelPart",
+        "properties_id"   : 0,
+        "Material"        : null
+    },{
+        "model_part_name" : "FluidModelPart.FluidParts_Fluid",
+        "properties_id"   : 1,
+        "Material"        : {
+            "constitutive_law" : {
+                "name" : "Newtonian2DLaw"
+            },
+            "Variables"        : {
+                "DENSITY"           : 1.0,
+                "DYNAMIC_VISCOSITY" : 0.000155
+            },
+            "Tables"           : null
+        }
+    }]
+}
diff --git a/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/MainKratos.py b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/MainKratos.py
new file mode 100755
index 00000000..3475e0fa
--- /dev/null
+++ b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/MainKratos.py
@@ -0,0 +1,46 @@
+import sys
+import math
+import time
+import importlib
+
+import KratosMultiphysics
+
+def CreateAnalysisStageWithFlushInstance(cls, global_model, parameters):
+    class AnalysisStageWithFlush(cls):
+
+        def __init__(self, model,project_parameters, flush_frequency=10.0):
+            super().__init__(model,project_parameters)
+            self.flush_frequency = flush_frequency
+            self.last_flush = time.time()
+            sys.stdout.flush()
+
+        def Initialize(self):
+            super().Initialize()
+            sys.stdout.flush()
+
+        def FinalizeSolutionStep(self):
+            super().FinalizeSolutionStep()
+
+            if self.parallel_type == "OpenMP":
+                now = time.time()
+                if now - self.last_flush > self.flush_frequency:
+                    sys.stdout.flush()
+                    self.last_flush = now
+
+    return AnalysisStageWithFlush(global_model, parameters)
+
+if __name__ == "__main__":
+
+    with open("ProjectParameters.json", 'r') as parameter_file:
+        parameters = KratosMultiphysics.Parameters(parameter_file.read())
+
+    analysis_stage_module_name = parameters["analysis_stage"].GetString()
+    analysis_stage_class_name = analysis_stage_module_name.split('.')[-1]
+    analysis_stage_class_name = ''.join(x.title() for x in analysis_stage_class_name.split('_'))
+
+    analysis_stage_module = importlib.import_module(analysis_stage_module_name)
+    analysis_stage_class = getattr(analysis_stage_module, analysis_stage_class_name)
+
+    global_model = KratosMultiphysics.Model()
+    simulation = CreateAnalysisStageWithFlushInstance(analysis_stage_class, global_model, parameters)
+    simulation.Run()
diff --git a/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/ProjectParameters.json b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/ProjectParameters.json
new file mode 100644
index 00000000..d6b58e29
--- /dev/null
+++ b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/ProjectParameters.json
@@ -0,0 +1,282 @@
+ {
+    "analysis_stage" : "KratosMultiphysics.FSIApplication.fsi_analysis",
+    "problem_data": {
+        "problem_name": "embedded_fsi_membrane_airfoil",
+        "parallel_type": "OpenMP",
+        "echo_level": 0,
+        "start_time": 0.0,
+        "end_time": 2.0e0
+    },
+    "solver_settings": {
+        "solver_type": "partitioned_embedded",
+        "coupling_scheme": "dirichlet_neumann",
+        "echo_level": 1,
+        "structure_solver_settings": {
+            "solver_type"                        : "Dynamic",
+            "model_part_name"                    : "Structure",
+            "domain_size"                        : 2,
+            "echo_level"                         : 0,
+            "analysis_type"                      : "non_linear",
+            "time_integration_method"            : "implicit",
+            "scheme_type"                        : "bossak",
+            "model_import_settings"              : {
+                "input_type": "mdpa",
+                "input_filename": "embedded_fsi_membrane_airfoil_structure"
+            },
+            "material_import_settings": {
+                "materials_filename": "StructuralMaterials.json"
+            },
+            "time_stepping": {
+                "time_step": 1.0e-2
+            },
+            "line_search"                        : false,
+            "convergence_criterion"              : "residual_criterion",
+            "displacement_relative_tolerance"    : 1e-5,
+            "displacement_absolute_tolerance"    : 1e-7,
+            "residual_relative_tolerance"        : 1e-5,
+            "residual_absolute_tolerance"        : 1e-7,
+            "max_iteration"                      : 50
+        },
+        "fluid_solver_settings":{
+            "model_part_name"             : "FluidModelPart",
+            "domain_size"                 : 2,
+            "solver_type"                 : "Embedded",
+            "model_import_settings"       : {
+                "input_type"     : "mdpa",
+                "input_filename" : "embedded_fsi_membrane_airfoil_fluid"
+            },
+            "material_import_settings": {
+                "materials_filename": "FluidMaterials.json"
+            },
+            "distance_modification_settings": {
+                "distance_threshold": 1.0e-3
+            },
+            "echo_level"                  : 0,
+            "compute_reactions"           : true,
+            "maximum_iterations"          : 50,
+            "relative_velocity_tolerance" : 1e-5,
+            "absolute_velocity_tolerance" : 1e-7,
+            "relative_pressure_tolerance" : 1e-5,
+            "absolute_pressure_tolerance" : 1e-7,
+            "assign_neighbour_elements_to_conditions" : true,
+            "volume_model_part_name"      : "FluidModelPart.FluidParts_Fluid",
+            "skin_parts"                  : ["FluidModelPart.AutomaticInlet2D_Inlet","FluidModelPart.Outlet2D_Outlet","FluidModelPart.VelocityConstraints2D_Walls"],
+            "no_skin_parts"               : [],
+            "time_stepping"               : {
+                "automatic_time_step": false,
+                "time_step": 1.0e-2
+            },
+            "formulation": {
+                "element_type": "embedded_weakly_compressible_navier_stokes_discontinuous",
+                "is_slip": true,
+                "slip_length": 1.0e1,
+                "penalty_coefficient": 1.0e2,
+                "dynamic_tau": 1.0
+            },
+            "fm_ale_settings": {
+                "fm_ale_step_frequency": 1,
+                "mesh_movement": "implicit",
+                "fm_ale_solver_settings": {
+                    "structure_model_part_name": "FSICouplingInterfaceFluid",
+                    "virtual_model_part_name": "VirtualModelPart",
+                    "linear_solver_settings": {
+                        "preconditioner_type": "amg",
+                        "solver_type": "amgcl",
+                        "smoother_type": "ilu0",
+                        "krylov_type": "cg",
+                        "max_iteration": 2000,
+                        "verbosity": 0,
+                        "tolerance": 1e-8,
+                        "scaling": false,
+                        "use_block_matrices_if_possible": true
+                    },
+                    "embedded_nodal_variable_settings": {
+                        "gradient_penalty_coefficient": 5.0e-2,
+                        "linear_solver_settings": {
+                            "preconditioner_type": "amg",
+                            "solver_type": "amgcl",
+                            "smoother_type": "ilu0",
+                            "krylov_type": "cg",
+                            "max_iteration": 2000,
+                            "verbosity": 0,
+                            "tolerance": 1e-8,
+                            "scaling": false,
+                            "block_size": 1,
+                            "use_block_matrices_if_possible": true
+                        }
+                    }
+                }
+            }
+        },
+        "coupling_settings":{
+            "nl_tol": 1e-4,
+            "nl_max_it": 10,
+            "coupling_strategy_settings": {
+                "solver_type": "MVQN",
+                "w_0": 0.5,
+                "abs_cut_off_tol" : 1e-6
+                // "solver_type": "MVQN_randomized_SVD",
+                // "abs_cut_off_tol" : 1e-6
+            },
+            "structure_interfaces_list": ["Structure.LinePressure2D_Load"]
+        }
+	},
+    "processes":{
+        "structure_constraints_process_list" : [{
+            "python_module" : "assign_vector_variable_process",
+            "kratos_module" : "KratosMultiphysics",
+            "process_name"  : "AssignVectorVariableProcess",
+            "Parameters"    : {
+                "model_part_name" : "Structure.DISPLACEMENT_EndPoints",
+                "variable_name"   : "DISPLACEMENT",
+                "interval"        : [0.0,"End"],
+                "constrained"     : [true,true,true],
+                "value"           : [0.0,0.0,0.0]
+            }
+        }],
+        "structure_loads_process_list"       : [],
+        "fluid_initial_conditions_process_list"  : [],
+        "fluid_boundary_conditions_process_list" : [{
+            "python_module" : "apply_inlet_process",
+            "kratos_module" : "KratosMultiphysics.FluidDynamicsApplication",
+            "process_name"  : "ApplyInletProcess",
+            "Parameters"    : {
+                "model_part_name" : "FluidModelPart.AutomaticInlet2D_Inlet",
+                "variable_name"   : "VELOCITY",
+                "interval"        : [0.0,1.0],
+                "modulus"         : "2.5833*t",
+                "direction"       : "automatic_inwards_normal"
+            }
+        },{
+            "python_module" : "apply_inlet_process",
+            "kratos_module" : "KratosMultiphysics.FluidDynamicsApplication",
+            "process_name"  : "ApplyInletProcess",
+            "Parameters"    : {
+                "model_part_name" : "FluidModelPart.AutomaticInlet2D_Inlet",
+                "variable_name"   : "VELOCITY",
+                "interval"        : [1.0,"End"],
+                "modulus"         : 2.5833,
+                "direction"       : "automatic_inwards_normal"
+            }
+        },{
+            "python_module" : "apply_outlet_process",
+            "kratos_module" : "KratosMultiphysics.FluidDynamicsApplication",
+            "process_name"  : "ApplyOutletProcess",
+            "Parameters"    : {
+                "model_part_name"    : "FluidModelPart.Outlet2D_Outlet",
+                "variable_name"      : "PRESSURE",
+                "constrained"        : true,
+                "value"              : 0.0,
+                "hydrostatic_outlet" : false,
+                "h_top"              : 0.0
+            }
+        },{
+            "python_module" : "assign_vector_variable_process",
+            "kratos_module" : "KratosMultiphysics",
+            "process_name"  : "AssignVectorVariableProcess",
+            "Parameters"    : {
+                "model_part_name" : "FluidModelPart.VelocityConstraints2D_Walls",
+                "variable_name"   : "VELOCITY",
+                "interval"        : [0.0,"End"],
+                "constrained"     : [false,true,false],
+                "value"           : [null,0.0,null]
+            }
+        },{
+            "python_module" : "assign_vector_variable_process",
+            "kratos_module" : "KratosMultiphysics",
+            "process_name"  : "AssignVectorVariableProcess",
+            "Parameters"    : {
+                "model_part_name" : "FluidModelPart.AutomaticInlet2D_Inlet",
+                "variable_name"   : "MESH_DISPLACEMENT",
+                "interval"        : [0.0,"End"],
+                "constrained"     : [true,true,false],
+                "value"           : [0.0,0.0,null]
+            }
+        },{
+            "python_module" : "assign_vector_variable_process",
+            "kratos_module" : "KratosMultiphysics",
+            "process_name"  : "AssignVectorVariableProcess",
+            "Parameters"    : {
+                "model_part_name" : "FluidModelPart.Outlet2D_Outlet",
+                "variable_name"   : "MESH_DISPLACEMENT",
+                "interval"        : [0.0,"End"],
+                "constrained"     : [true,true,false],
+                "value"           : [0.0,0.0,null]
+            }
+        },{
+            "python_module" : "assign_vector_variable_process",
+            "kratos_module" : "KratosMultiphysics",
+            "process_name"  : "AssignVectorVariableProcess",
+            "Parameters"    : {
+                "model_part_name" : "FluidModelPart.VelocityConstraints2D_Walls",
+                "variable_name"   : "MESH_DISPLACEMENT",
+                "interval"        : [0.0,"End"],
+                "constrained"     : [true,true,false],
+                "value"           : [0.0,0.0,null]
+            }
+        }],
+        "fluid_gravity" : [],
+        "fluid_auxiliar_process_list" : []
+    },
+    "output_processes":{
+        "gid_output" : [{
+            "python_module" : "gid_output_process",
+            "kratos_module" : "KratosMultiphysics",
+            "process_name"  : "GiDOutputProcess",
+            "Parameters"    : {
+                "model_part_name"        : "Structure",
+                "output_name"            : "embedded_fsi_membrane_airfoil_structure",
+                "postprocess_parameters" : {
+                    "result_file_configuration" : {
+                        "gidpost_flags"       : {
+                            "GiDPostMode"           : "GiD_PostBinary",
+                            "WriteDeformedMeshFlag" : "WriteDeformed",
+                            "WriteConditionsFlag"   : "WriteConditions",
+                            "MultiFileFlag"         : "SingleFile"
+                        },
+                        "file_label"          : "time",
+                        "output_control_type" : "step",
+                        "output_interval"     : 1,
+                        "body_output"         : true,
+                        "node_output"         : false,
+                        "skin_output"         : false,
+                        "plane_output"        : [],
+                        "nodal_results"       : ["DISPLACEMENT","VELOCITY","ACCELERATION","REACTION","LINE_LOAD"],
+                        "gauss_point_results" : []
+                    },
+                    "point_data_configuration"  : []
+                }
+            }
+        },{
+            "python_module": "gid_output_process",
+            "kratos_module": "KratosMultiphysics",
+            "process_name": "GiDOutputProcess",
+            "Parameters": {
+                "model_part_name": "FluidModelPart.FluidParts_Fluid",
+                "output_name": "embedded_fsi_membrane_airfoil_fluid",
+                "postprocess_parameters": {
+                    "result_file_configuration": {
+                        "gidpost_flags": {
+                            "GiDPostMode": "GiD_PostBinary",
+                            "WriteDeformedMeshFlag": "WriteDeformed",
+                            "WriteConditionsFlag": "WriteConditions",
+                            "MultiFileFlag": "SingleFile"
+                        },
+                        "file_label": "time",
+                        "output_control_type": "step",
+                        "output_interval" : 1,
+                        "body_output": true,
+                        "node_output": false,
+                        "skin_output": false,
+                        "plane_output": [],
+                        "nodal_results": ["VELOCITY","PRESSURE","MESH_VELOCITY"],
+                        "nodal_nonhistorical_results": [],
+                        "elemental_conditional_flags_results": [],
+                        "gauss_point_results": []
+                    },
+                    "point_data_configuration": []
+                }
+            }
+        }]
+    }
+}
diff --git a/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/StructuralMaterials.json b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/StructuralMaterials.json
new file mode 100644
index 00000000..b78a6b5b
--- /dev/null
+++ b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/StructuralMaterials.json
@@ -0,0 +1,15 @@
+{
+    "properties" : [{
+        "model_part_name" : "Structure.Parts_Cable_Membrane",
+        "properties_id"   : 1,
+        "Material"        : {
+            "Variables"        : {
+                "DENSITY"             : 441.75,
+                "YOUNG_MODULUS"       : 250000.0,
+                "THICKNESS"           : 0.0002,
+                "PRESTRESS_VECTOR"    : [0.0]
+            },
+            "Tables"           : null
+        }
+    }]
+}
diff --git a/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/embedded_fsi_membrane_airfoil_fluid.mdpa b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/embedded_fsi_membrane_airfoil_fluid.mdpa
new file mode 100644
index 00000000..902395de
--- /dev/null
+++ b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/embedded_fsi_membrane_airfoil_fluid.mdpa
@@ -0,0 +1,434113 @@
+Begin ModelPartData
+//  VARIABLE_NAME value
+End ModelPartData
+
+Begin Properties 0
+End Properties
+
+Begin Nodes
+    1   2.4000000000  -1.2000000000   0.0000000000
+    2   2.3750000000  -1.2000000000   0.0000000000
+    3   2.4000000000  -1.1750000000   0.0000000000
+    4   2.3792666667  -1.1720599802   0.0000000000
+    5   2.3552777778  -1.1789387716   0.0000000000
+    6   2.3500000000  -1.2000000000   0.0000000000
+    7   2.4000000000  -1.1500000000   0.0000000000
+    8   2.3660555556  -1.1563611294   0.0000000000
+    9   2.3761277778  -1.1375289364   0.0000000000
+   10   2.3300462963  -1.1800578470   0.0000000000
+   11   2.3375000001  -1.1599192252   0.0000000000
+   12   2.3250000000  -1.2000000000   0.0000000000
+   13   2.4000000000  -1.1250000000   0.0000000000
+   14   2.3500000001  -1.1382685901   0.0000000000
+   15   2.3645833334  -1.1180149625   0.0000000000
+   16   2.3098688272  -1.1587726409   0.0000000000
+   17   2.3000000000  -1.2000000000   0.0000000000
+   18   2.4000000000  -1.1000000000   0.0000000000
+   19   2.3211319016  -1.1371808805   0.0000000000
+   20   2.3000000001  -1.1815698603   0.0000000000
+   21   2.3375000001  -1.1166179550   0.0000000000
+   22   2.3750000001  -1.0949673199   0.0000000000
+   23   2.3500000001  -1.0949673199   0.0000000000
+   24   2.2750000000  -1.2000000000   0.0000000000
+   25   2.4000000000  -1.0750000000   0.0000000000
+   26   2.2919225823  -1.1361094122   0.0000000000
+   27   2.3063424140  -1.1150033086   0.0000000000
+   28   2.2791666667  -1.1577722283   0.0000000000
+   29   2.3250000001  -1.0949673199   0.0000000000
+   30   2.3625000001  -1.0733166848   0.0000000000
+   31   2.2625000000  -1.1783493649   0.0000000000
+   32   2.3375000001  -1.0733166848   0.0000000000
+   33   2.2500000000  -1.2000000000   0.0000000000
+   34   2.4000000000  -1.0500000000   0.0000000000
+   35   2.3750000001  -1.0516660497   0.0000000000
+   36   2.2750000000  -1.1133974596   0.0000000000
+   37   2.2625000000  -1.1350480947   0.0000000000
+   38   2.3125000001  -1.0733166848   0.0000000000
+   39   2.2500000000  -1.1566987298   0.0000000000
+   40   2.2875000000  -1.0917468245   0.0000000000
+   41   2.3500000001  -1.0516660497   0.0000000000
+   42   2.2375000000  -1.1783493649   0.0000000000
+   43   2.3250000001  -1.0516660497   0.0000000000
+   44   2.2500000000  -1.1133974596   0.0000000000
+   45   2.3645833334  -1.0291795122   0.0000000000
+   46   2.2250000000  -1.2000000000   0.0000000000
+   47   2.2625000000  -1.0917468245   0.0000000000
+   48   2.4000000000  -1.0250000000   0.0000000000
+   49   2.2375000000  -1.1350480947   0.0000000000
+   50   2.3000000001  -1.0516660497   0.0000000000
+   51   2.2250000000  -1.1566987298   0.0000000000
+   52   2.2750000000  -1.0700961894   0.0000000000
+   53   2.3375000001  -1.0300154146   0.0000000000
+   54   2.2125000000  -1.1783493649   0.0000000000
+   55   2.3125000001  -1.0300154146   0.0000000000
+   56   2.3750000001  -1.0083647795   0.0000000000
+   57   2.2250000000  -1.1133974596   0.0000000000
+   58   2.2375000000  -1.0917468245   0.0000000000
+   59   2.2510416667  -1.0703645640   0.0000000000
+   60   2.3500000001  -1.0083647795   0.0000000000
+   61   2.2125000000  -1.1350480947   0.0000000000
+   62   2.2687500000  -1.0500558020   0.0000000000
+   63   2.2000000000  -1.2000000000   0.0000000000
+   64   2.4000000000  -1.0000000000   0.0000000000
+   65   2.2875000001  -1.0300154146   0.0000000000
+   66   2.2000000000  -1.1566987298   0.0000000000
+   67   2.3250000001  -1.0083647795   0.0000000000
+   68   2.1875000000  -1.1783493649   0.0000000000
+   69   2.3696428572  -0.9869386746   0.0000000000
+   70   2.3000000001  -1.0083647795   0.0000000000
+   71   2.2125000000  -1.0917468245   0.0000000000
+   72   2.2000000000  -1.1133974596   0.0000000000
+   73   2.2250000000  -1.0700961894   0.0000000000
+   74   2.2625000001  -1.0300154146   0.0000000000
+   75   2.2375000000  -1.0484455543   0.0000000000
+   76   2.1875000000  -1.1350480947   0.0000000000
+   77   2.3375000001  -0.9867141445   0.0000000000
+   78   2.1750000000  -1.2000000000   0.0000000000
+   79   2.4000000000  -0.9750000000   0.0000000000
+   80   2.2750000001  -1.0083647795   0.0000000000
+   81   2.1750000000  -1.1566987298   0.0000000000
+   82   2.3125000001  -0.9867141445   0.0000000000
+   83   2.3768452381  -0.9643025825   0.0000000000
+   84   2.2000000000  -1.0700961894   0.0000000000
+   85   2.1875000000  -1.0917468245   0.0000000000
+   86   2.1625000000  -1.1783493649   0.0000000000
+   87   2.2135416667  -1.0487139290   0.0000000000
+   88   2.3500000001  -0.9650635094   0.0000000000
+   89   2.2312500000  -1.0284051669   0.0000000000
+   90   2.1750000000  -1.1133974596   0.0000000000
+   91   2.2875000001  -0.9867141445   0.0000000000
+   92   2.2500000001  -1.0083647796   0.0000000000
+   93   2.1625000000  -1.1350480947   0.0000000000
+   94   2.3250000001  -0.9650635094   0.0000000000
+   95   2.1500000000  -1.2000000000   0.0000000000
+   96   2.4000000000  -0.9500000000   0.0000000000
+   97   2.1500000000  -1.1566987298   0.0000000000
+   98   2.2625000001  -0.9867141445   0.0000000000
+   99   2.3000000001  -0.9650635094   0.0000000000
+  100   2.3645833334  -0.9445107286   0.0000000000
+  101   2.2250000001  -1.0083647796   0.0000000000
+  102   2.1750000000  -1.0700961894   0.0000000000
+  103   2.1875000000  -1.0484455543   0.0000000000
+  104   2.1625000000  -1.0917468245   0.0000000000
+  105   2.1375000000  -1.1783493649   0.0000000000
+  106   2.3375000001  -0.9434128743   0.0000000000
+  107   2.2000000000  -1.0267949192   0.0000000000
+  108   2.1500000000  -1.1133974596   0.0000000000
+  109   2.2750000001  -0.9650635094   0.0000000000
+  110   2.2375000001  -0.9867141445   0.0000000000
+  111   2.1375000000  -1.1350480947   0.0000000000
+  112   2.3125000001  -0.9434128743   0.0000000000
+  113   2.1250000000  -1.2000000000   0.0000000000
+  114   2.4000000000  -0.9250000000   0.0000000000
+  115   2.1250000000  -1.1566987298   0.0000000000
+  116   2.2500000001  -0.9650635094   0.0000000000
+  117   2.3750000001  -0.9217622392   0.0000000000
+  118   2.2875000001  -0.9434128743   0.0000000000
+  119   2.1625000000  -1.0484455543   0.0000000000
+  120   2.1500000000  -1.0700961894   0.0000000000
+  121   2.3500000001  -0.9217622392   0.0000000000
+  122   2.1750000000  -1.0267949192   0.0000000000
+  123   2.1375000000  -1.0917468245   0.0000000000
+  124   2.2125000001  -0.9867141445   0.0000000000
+  125   2.3250000001  -0.9217622392   0.0000000000
+  126   2.1875000000  -1.0051442841   0.0000000000
+  127   2.1125000000  -1.1783493649   0.0000000000
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+End Nodes
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+End Conditions
+
+Begin SubModelPart FluidParts_Fluid // Group Fluid // Subtree FluidParts
+    Begin SubModelPartNodes
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+    Begin SubModelPartNodes
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+    Begin SubModelPartElements
+    End SubModelPartElements
+    Begin SubModelPartConditions
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+    End SubModelPartConditions
+End SubModelPart
+Begin SubModelPart Outlet2D_Outlet // Group Outlet // Subtree Outlet2D
+    Begin SubModelPartNodes
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+    End SubModelPartNodes
+    Begin SubModelPartElements
+    End SubModelPartElements
+    Begin SubModelPartConditions
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+    End SubModelPartConditions
+End SubModelPart
+Begin SubModelPart VelocityConstraints2D_Walls // Group Walls // Subtree VelocityConstraints2D
+    Begin SubModelPartNodes
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+    End SubModelPartNodes
+End SubModelPart
diff --git a/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/embedded_fsi_membrane_airfoil_structure.mdpa b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/embedded_fsi_membrane_airfoil_structure.mdpa
new file mode 100644
index 00000000..e54eefaf
--- /dev/null
+++ b/fluid_structure_interaction/validation/embedded_fsi_membrane_airfoil/source/embedded_fsi_membrane_airfoil_structure.mdpa
@@ -0,0 +1,933 @@
+Begin ModelPartData
+//  VARIABLE_NAME value
+End ModelPartData
+
+Begin Properties 0
+End Properties
+Begin Nodes
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diff --git a/fluid_structure_interaction/validation/embedded_fsi_mixer_Y/README.md b/fluid_structure_interaction/validation/embedded_fsi_mixer_Y/README.md
index 8a0f4cb7..e749b289 100644
--- a/fluid_structure_interaction/validation/embedded_fsi_mixer_Y/README.md
+++ b/fluid_structure_interaction/validation/embedded_fsi_mixer_Y/README.md
@@ -7,7 +7,7 @@
 **Source files:** [Mixer with flexible blades](https://github.com/KratosMultiphysics/Examples/tree/master/fluid_structure_interaction/validation/embedded_fsi_mixer_Y/source)
 
 ## Case Specification
-This example is specifically conceived to prove the extended scope of applicatoin of embedded mesh methods. Hence, it involves extremely large rotations, which would be impossible to solve by using a body fitted ALE based approach.
+This example is specifically conceived to prove the extended scope of application of embedded mesh methods. Hence, it involves extremely large rotations, which would be impossible to solve by using a body fitted ALE based approach.
 
 The problem is set up as a 2D idealization of a turbine mixer with clockwise-anticlockwise alternate rotation. The problem geometry is a unit diameter circle with three embedded flexible blades. An imposed rotation is enforced in the blades axis to emulate the spin of the rotor. Such rotation changes the direction (anticlockwise to clockwise and viceversa) after More details on the dimensions, material settings and boundary conditions can be found in [here](https://doi.org/10.1016/j.cma.2020.113179).