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Advection diffusion in multi-domain #111

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8dbd0d1
added example
RemDelaporteMathurin Jul 21, 2025
a43c304
Merge branch 'festim2' into advection-diffusion-multi
RemDelaporteMathurin Jul 21, 2025
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3 changes: 2 additions & 1 deletion book/_toc.yml
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Original file line number Diff line number Diff line change
Expand Up @@ -30,4 +30,5 @@ parts:
- file: content/applications/task08
- file: content/applications/task09
- file: content/applications/task06
- file: content/applications/task10
- file: content/applications/task10
- file: content/advection
389 changes: 389 additions & 0 deletions book/content/advection.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"id": "b782b819",
"metadata": {},
"source": [
"# Advection-diffusion problem (multi-material)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "e4509407",
"metadata": {},
"outputs": [],
"source": [
"from mpi4py import MPI\n",
"\n",
"import dolfinx\n",
"import numpy as np\n",
"import basix\n",
"import festim as F\n",
"\n",
"n =50\n",
"\n",
"def bottom_boundary(x):\n",
" return np.isclose(x[1], 0.0)\n",
"\n",
"def top_boundary(x):\n",
" return np.isclose(x[1], 1.0)\n",
"\n",
"def bottom_left_boundary(x):\n",
" return np.logical_and(np.isclose(x[0], 0.0), x[1] <= 0.5 + 1e-14)\n",
"\n",
"def half(x):\n",
" return x[1] <= 0.5 + 1e-14\n",
"\n",
"mesh = dolfinx.mesh.create_unit_square(\n",
" MPI.COMM_WORLD, n, n, dolfinx.mesh.CellType.triangle\n",
")\n",
"\n",
"# Split domain in half and set an interface tag of 5\n",
"gdim = mesh.geometry.dim\n",
"tdim = mesh.topology.dim\n",
"fdim = tdim - 1\n",
"top_facets = dolfinx.mesh.locate_entities_boundary(mesh, fdim, top_boundary)\n",
"bottom_facets = dolfinx.mesh.locate_entities_boundary(mesh, fdim, bottom_boundary)\n",
"bot_left_facets = dolfinx.mesh.locate_entities_boundary(\n",
" mesh, fdim, bottom_left_boundary\n",
")\n",
"num_facets_local = (\n",
" mesh.topology.index_map(fdim).size_local\n",
" + mesh.topology.index_map(fdim).num_ghosts\n",
")\n",
"facets = np.arange(num_facets_local, dtype=np.int32)\n",
"values = np.full_like(facets, 0, dtype=np.int32)\n",
"values[top_facets] = 1\n",
"values[bottom_facets] = 2\n",
"values[bot_left_facets] = 3\n",
"\n",
"bottom_cells = dolfinx.mesh.locate_entities(mesh, tdim, half)\n",
"num_cells_local = (\n",
" mesh.topology.index_map(tdim).size_local\n",
" + mesh.topology.index_map(tdim).num_ghosts\n",
")\n",
"cells = np.full(num_cells_local, 5, dtype=np.int32)\n",
"cells[bottom_cells] = 4\n",
"ct = dolfinx.mesh.meshtags(\n",
" mesh, tdim, np.arange(num_cells_local, dtype=np.int32), cells\n",
")\n",
"all_b_facets = dolfinx.mesh.compute_incident_entities(\n",
" mesh.topology, ct.find(4), tdim, fdim\n",
")\n",
"all_t_facets = dolfinx.mesh.compute_incident_entities(\n",
" mesh.topology, ct.find(5), tdim, fdim\n",
")\n",
"interface = np.intersect1d(all_b_facets, all_t_facets)\n",
"values[interface] = 6\n",
"\n",
"mt = dolfinx.mesh.meshtags(mesh, mesh.topology.dim - 1, facets, values)\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "a91742d1",
"metadata": {},
"outputs": [],
"source": [
"def create_velocity_field():\n",
" def velocity_func(x):\n",
" values = np.zeros((2, x.shape[1])) # Initialize with zeros\n",
" scalar_value = -1000 * x[1] * (x[1] - 0.5) # Compute the scalar function\n",
" values[0] = scalar_value # Assign to first component\n",
" values[1] = 0 # Second component remains zero\n",
" return values\n",
"\n",
" submesh, submesh_to_mesh, v_map = dolfinx.mesh.create_submesh(\n",
" mesh, ct.dim, ct.find(4)\n",
" )[0:3]\n",
" v_cg = basix.ufl.element(\n",
" \"Lagrange\", submesh.topology.cell_name(), 2, shape=(submesh.geometry.dim,)\n",
" )\n",
" V_velocity = dolfinx.fem.functionspace(submesh, v_cg)\n",
" u = dolfinx.fem.Function(V_velocity)\n",
" u.interpolate(velocity_func)\n",
" return u\n",
"\n",
"\n",
"u = create_velocity_field()\n",
"\n",
"writer = dolfinx.io.VTXWriter(MPI.COMM_WORLD, \"velocity.bp\", u, engine=\"BP5\")\n",
"writer.write(t=0)\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "c2a88a52",
"metadata": {},
"outputs": [],
"source": [
"from dolfinx import plot\n",
"import pyvista\n",
"\n",
"pyvista.start_xvfb()\n",
"pyvista.set_jupyter_backend(\"html\")"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "42c527ce",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "ec6a05530c26467c8338481a55dcb5f5",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"EmbeddableWidget(value='<iframe srcdoc=\"<!DOCTYPE html>\\n<html>\\n <head>\\n <meta http-equiv=&quot;Content-…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"topology, cell_types, geometry = plot.vtk_mesh(u.function_space)\n",
"values = np.zeros((geometry.shape[0], 3), dtype=np.float64)\n",
"values[:, :len(u)] = u.x.array.real.reshape((geometry.shape[0], len(u)))\n",
"\n",
"# Create a point cloud of glyphs\n",
"function_grid = pyvista.UnstructuredGrid(topology, cell_types, geometry)\n",
"function_grid[\"v\"] = values\n",
"glyphs = function_grid.glyph(orient=\"v\", factor=0.0005)\n",
"\n",
"# Create a pyvista-grid for the mesh\n",
"grid = pyvista.UnstructuredGrid(*plot.vtk_mesh(mesh, mesh.topology.dim))\n",
"\n",
"# Create plotter\n",
"plotter = pyvista.Plotter()\n",
"plotter.add_mesh(grid, style=\"wireframe\", color=\"k\", opacity=0.1)\n",
"plotter.add_mesh(glyphs)\n",
"plotter.view_xy()\n",
"if not pyvista.OFF_SCREEN:\n",
" plotter.show()\n",
"else:\n",
" fig_as_array = plotter.screenshot(\"glyphs.png\")"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "1fe8218b",
"metadata": {},
"outputs": [],
"source": [
"my_model = F.HydrogenTransportProblemDiscontinuous()\n",
"my_model.mesh = F.Mesh(mesh)\n",
"my_model.volume_meshtags = ct\n",
"my_model.facet_meshtags = mt\n",
"\n",
"material_bottom = F.Material(D_0=0.5, E_D=0 * 0.1)\n",
"material_top = F.Material(D_0=0.5, E_D=0 * 0.1)\n",
"\n",
"material_bottom.K_S_0 = 2.0\n",
"material_bottom.E_K_S = 0\n",
"material_top.K_S_0 = 6.0\n",
"material_top.E_K_S = 0\n",
"\n",
"top_domain = F.VolumeSubdomain(5, material=material_top)\n",
"bottom_domain = F.VolumeSubdomain(4, material=material_bottom)\n",
"\n",
"top_surface = F.SurfaceSubdomain(id=1)\n",
"bottom_surface = F.SurfaceSubdomain(id=2)\n",
"inlet_surf = F.SurfaceSubdomain(id=3)\n",
"my_model.subdomains = [\n",
" bottom_domain,\n",
" top_domain,\n",
" top_surface,\n",
" bottom_surface,\n",
" inlet_surf,\n",
"]\n",
"\n",
"my_model.interfaces = [F.Interface(6, (bottom_domain, top_domain), penalty_term=5000)]\n",
"\n",
"my_model.surface_to_volume = {\n",
" top_surface: top_domain,\n",
" bottom_surface: bottom_domain,\n",
" inlet_surf: bottom_domain,\n",
"}\n",
"\n",
"H = F.Species(\"H\", mobile=True)\n",
"\n",
"my_model.species = [H]\n",
"\n",
"for species in my_model.species:\n",
" species.subdomains = [bottom_domain, top_domain]\n",
"\n",
"\n",
"my_model.boundary_conditions = [\n",
" F.FixedConcentrationBC(top_surface, value=0.0, species=H),\n",
" F.FixedConcentrationBC(inlet_surf, value=1.0, species=H),\n",
" F.FixedConcentrationBC(bottom_surface, value=0.0, species=H),\n",
"]\n",
"\n",
"my_model.advection_terms = [\n",
" F.AdvectionTerm(velocity=u, species=[H], subdomain=bottom_domain)\n",
"]\n",
"\n",
"\n",
"my_model.temperature = 500.0\n",
"\n",
"my_model.settings = F.Settings(atol=1e-10, rtol=1e-10, transient=False)\n",
"\n",
"my_model.exports = [\n",
" F.VTXSpeciesExport(f\"u_{subdomain.id}.bp\", field=H, subdomain=subdomain)\n",
" for subdomain in my_model.volume_subdomains\n",
"]\n",
"\n",
"my_model.initialise()\n",
"my_model.run()\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "55fa771a",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "96402a37d52f413ab81b52d14c693437",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"EmbeddableWidget(value='<iframe srcdoc=\"<!DOCTYPE html>\\n<html>\\n <head>\\n <meta http-equiv=&quot;Content-…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def plot_in_one_subdomain(subdomain, species, label=\"c\"):\n",
" u = species.subdomain_to_post_processing_solution[subdomain]\n",
" topology, cell_types, geometry = plot.vtk_mesh(u.function_space)\n",
" u_grid = pyvista.UnstructuredGrid(topology, cell_types, geometry)\n",
" u_grid.point_data[label] = u.x.array.real\n",
" u_grid.set_active_scalars(label)\n",
" return u_grid\n",
"\n",
"u_plotter = pyvista.Plotter()\n",
"\n",
"for subdomain in my_model.volume_subdomains:\n",
" u_grid = plot_in_one_subdomain(subdomain, H)\n",
" u_plotter.add_mesh(u_grid, cmap=\"viridis\", show_edges=False)\n",
" u_plotter.add_mesh(u_grid, style=\"wireframe\", color=\"white\", opacity=0.1)\n",
" u_plotter.view_xy()\n",
"\n",
"if not pyvista.OFF_SCREEN:\n",
" u_plotter.show()\n",
"else:\n",
" figure = u_plotter.screenshot(\"concentration.png\")"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "23b30e74",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "2aa9b335a45949898de63103551d5efa",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"EmbeddableWidget(value='<iframe srcdoc=\"<!DOCTYPE html>\\n<html>\\n <head>\\n <meta http-equiv=&quot;Content-…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"u_plotter = pyvista.Plotter()\n",
"\n",
"u_grid = plot_in_one_subdomain(my_model.volume_subdomains[0], H)\n",
"u_grid.set_active_scalars(\"c\")\n",
"u_plotter.add_mesh(u_grid, cmap=\"viridis\", show_edges=False)\n",
"u_plotter.add_mesh(u_grid, style=\"wireframe\", color=\"white\", opacity=0.1)\n",
"u_plotter.view_xy()\n",
"\n",
"if not pyvista.OFF_SCREEN:\n",
" u_plotter.show()\n",
"else:\n",
" figure = u_plotter.screenshot(\"concentration.png\")"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "725fe826",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "7507c1e5d95c47b585108f7c0e3e878b",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"EmbeddableWidget(value='<iframe srcdoc=\"<!DOCTYPE html>\\n<html>\\n <head>\\n <meta http-equiv=&quot;Content-…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"u_plotter = pyvista.Plotter()\n",
"\n",
"u_grid = plot_in_one_subdomain(my_model.volume_subdomains[1], H)\n",
"u_grid.set_active_scalars(\"c\")\n",
"u_plotter.add_mesh(u_grid, cmap=\"viridis\", show_edges=False)\n",
"u_plotter.add_mesh(u_grid, style=\"wireframe\", color=\"white\", opacity=0.1)\n",
"u_plotter.view_xy()\n",
"\n",
"if not pyvista.OFF_SCREEN:\n",
" u_plotter.show()\n",
"else:\n",
" figure = u_plotter.screenshot(\"concentration.png\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "festim-workshop",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.13.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}