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Merge pull request #155 from KratosMultiphysics/PR_conv_diff_3d
[IgaApplication] 3d laplacian problem sbm
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‎iga/README.md‎

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# Iga Examples
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## Use Cases
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- [External Boundary Circle (NURBS) ](https://github.com/KratosMultiphysics/Examples/blob/master/iga/use_cases/external_boundary_cirle_with_nurbs/README.md)
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- [External Boundary Circle (NURBS)](https://github.com/KratosMultiphysics/Examples/blob/master/iga/use_cases/external_boundary_circle_with_nurbs/README.md)
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- [IGA Single-Patch Shell in Membrane Action with Weak Supports and Line Load](https://github.com/KratosMultiphysics/Examples/blob/master/iga/use_cases/iga_shell_3p_single_patch/README.md)
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- [3D Laplacian on an Embedded Cube with SBM](https://github.com/KratosMultiphysics/Examples/blob/master/iga/use_cases/laplacian_3d_cube_sbm/README.md)
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## Validation Cases
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‎iga/use_cases/laplacian_sbm_3d_bunny/ProjectParameters.json‎

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{
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"problem_data": {
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"problem_name": "laplacian_3d_stanford_bunny",
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"echo_level": 1,
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"parallel_type": "OpenMP",
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"start_time": 0.0,
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"end_time": 1.0
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},
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"solver_settings": {
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"solver_type": "stationary",
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"analysis_type": "non_linear",
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"model_part_name": "IgaModelPart",
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"domain_size": 3,
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"model_import_settings": {
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"input_type": "use_input_model_part"
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},
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"material_import_settings": {
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"materials_filename": "materials.json"
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},
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"linear_solver_settings": {
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"solver_type": "skyline_lu_factorization"
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},
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"skip_entities_replace_and_check": true,
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"line_search": false,
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"echo_level": 1,
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"compute_reactions": false,
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"max_iteration": 3,
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"solution_relative_tolerance": 1e-14,
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"solution_absolute_tolerance": 1e-14,
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"residual_relative_tolerance": 1e-14,
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"residual_absolute_tolerance": 1e-14,
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"time_stepping": {
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"time_step": 1e20
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}
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},
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"modelers": [
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{
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"modeler_name": "import_mdpa_modeler",
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"kratos_module": "KratosMultiphysics",
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"Parameters": {
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"input_filename": "bunny",
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"model_part_name": "initial_skin_model_part_out"
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}
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},
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{
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"modeler_name": "NurbsGeometryModelerSbm",
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"Parameters": {
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"model_part_name": "IgaModelPart",
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"lower_point_xyz": [0.0, 0.0, 0.0],
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"upper_point_xyz": [2.0, 2.0, 2.0],
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"lower_point_uvw": [0.0, 0.0, 0.0],
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"upper_point_uvw": [2.0, 2.0, 2.0],
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"polynomial_order": [2, 2, 2],
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"number_of_knot_spans": [40, 40, 40],
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"lambda_outer": 1.0,
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"lambda_inner": 0.5,
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"number_of_inner_loops": 0,
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"skin_model_part_outer_initial_name": "initial_skin_model_part_out",
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"skin_model_part_name": "skin_model_part"
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}
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},
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{
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"modeler_name": "IgaModelerSbm",
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"Parameters": {
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"echo_level": 0,
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"skin_model_part_name": "skin_model_part",
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"analysis_model_part_name": "IgaModelPart",
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"element_condition_list": [
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{
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"geometry_type": "GeometryVolume",
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"iga_model_part": "ConvectionDiffusionDomain",
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"type": "element",
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"name": "LaplacianElement",
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"shape_function_derivatives_order": 2
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},
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{
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"geometry_type": "SurfaceEdge",
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"iga_model_part": "SBM_Support_outer",
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"type": "condition",
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"name": "SbmLaplacianConditionDirichlet",
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"shape_function_derivatives_order": 10,
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"sbm_parameters": {
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"is_inner": false
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}
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}
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]
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}
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}
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],
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"processes": {
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"additional_processes": [
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{
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"python_module": "assign_iga_external_conditions_process",
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"kratos_module": "KratosMultiphysics.IgaApplication",
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"process_name": "AssignIgaExternalConditionsProcess",
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"Parameters": {
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"echo_level": 0,
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"model_part_name": "IgaModelPart",
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"element_condition_list": [
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{
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"iga_model_part": "IgaModelPart.ConvectionDiffusionDomain",
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"variables": [
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{
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"variable_name": "HEAT_FLUX",
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"value": "sin(x) * sinh(y) * cos(z)"
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}
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]
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},
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{
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"iga_model_part": "IgaModelPart.SBM_Support_outer",
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"variables": [
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{
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"variable_name": "TEMPERATURE",
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"value": "sin(x) * sinh(y) * cos(z)"
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}
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]
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}
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]
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}
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}
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],
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"dirichlet_process_list": [
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{
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"kratos_module": "KratosMultiphysics",
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"python_module": "assign_scalar_variable_to_nodes_process",
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"Parameters": {
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"model_part_name": "skin_model_part.outer",
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"variable_name": "TEMPERATURE",
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"value": "sin(x) * sinh(y) * cos(z)"
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}
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}
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],
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"constraints_process_list": []
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},
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"output_processes": {
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"output_process_list": []
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}
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}

‎iga/use_cases/laplacian_sbm_3d_bunny/README.md‎

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# Use Case IGA - 3D Laplacian on the Stanford Bunny with SBM
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Short description
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This example solves a stationary 3D Laplacian problem with the Surrogate Boundary Method (SBM) in the IGA Application. The embedded boundary is the Stanford bunny imported from `bunny.mdpa`, while the analysis is carried out on a structured background NURBS volume.
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The manufactured solution used for validation is:
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`T(x, y, z) = sin(x) * sinh(y) * cos(z)`
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The same field is prescribed on the surrogate boundary, and the corresponding volumetric term is assigned through `HEAT_FLUX`.
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Files
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- `ProjectParameters.json`
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- `materials.json`
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- `bunny.mdpa`
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- `run_and_post.py`
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- `convergence.py`
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- `plot_conditions.py`
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Geometry
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- `import_mdpa_modeler` loads the Stanford bunny skin into `initial_skin_model_part_out`.
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- `NurbsGeometryModelerSbm` creates the background volume on `[0, 2]^3` with order `[2, 2, 2]` and a structured knot-span grid.
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- `IgaModelerSbm` creates:
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- `LaplacianElement` on `IgaModelPart.ConvectionDiffusionDomain`
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- `SbmLaplacianConditionDirichlet` on `IgaModelPart.SBM_Support_outer`
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Solver
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- Stationary convection-diffusion analysis
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- 3D Laplacian formulation
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- SBM Dirichlet condition with `PENALTY_FACTOR = -1`
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- Linear solver: `skyline_lu_factorization`
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Run
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```bash
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python3 run_and_post.py
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python3 convergence.py
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python3 plot_conditions.py
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```
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`run_and_post.py` runs the analysis, prints the absolute and normalized L2 errors, and plots the error distribution at the element integration points.
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`convergence.py` performs a mesh-refinement study by changing the number of knot spans of the background NURBS volume.
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`plot_conditions.py` initializes the model and plots the outer surrogate boundary in 3D using three gray tones according to the face orientation.

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