Add lid driven cavity as first example

- Can maybe used later to compare against torrilhon2013

fenicsR13/examples/lid_driven_cavity/create_mesh.py

+#!/usr/bin/env python3
+
+"Script to generate a set of ring meshes"
+
+import os
+import dolfin as df
+
+GMSH_PATH = "gmsh"
+GEO_NAME = "lid"
+
+def create_mesh(exponent):
+    "Generates a mesh using gmsh"
+
+    mesh_name = "{}{}".format(GEO_NAME, exponent)
+
+    os.system(
+        "{} -setnumber p {} -2 -o {}.msh {}.geo".format(
+            GMSH_PATH, exponent, mesh_name, GEO_NAME))
+
+    os.system("dolfin-convert {0}.msh {0}.xml".format(mesh_name))
+
+    mesh = df.Mesh("{}.xml".format(mesh_name))
+    subdomains = df.MeshFunction(
+        "size_t", mesh, "{}_physical_region.xml".format(mesh_name))
+    boundaries = df.MeshFunction(
+        "size_t", mesh, "{}_facet_region.xml".format(mesh_name))
+
+    file = df.HDF5File(mesh.mpi_comm(), "{}.h5".format(mesh_name), "w")
+    file.write(mesh, "/mesh")
+    file.write(subdomains, "/subdomains")
+    file.write(boundaries, "/boundaries")
+
+    return (mesh, subdomains, boundaries)
+
+for p in range(0+1, 5+1):
+    create_mesh(p)

fenicsR13/examples/lid_driven_cavity/input.yml

+# Case name, used as output folder
+case_name: lid_driven_cavity
+
+# Meshes
+# ======
+# Input files in h5 format.
+# List containing one or more meshes to perform simulation on.
+meshes:
+  # - lid0.h5
+  # - lid1.h5
+  # - lid2.h5
+  # - lid3.h5
+  # - lid4.h5
+  - lid5.h5
+  # - lid6.h5
+  # - lid7.h5
+  # - lid6.h5
+
+elements:
+  "theta":
+    "shape": "Lagrange"
+    "degree": 1
+  "s":
+    "shape": "Lagrange"
+    "degree": 1
+  "p":
+    "shape": "Lagrange"
+    "degree": 1
+  "u":
+    "shape": "Lagrange"
+    "degree": 1
+  "sigma":
+    "shape": "Lagrange"
+    "degree": 1
+
+# Stabilization
+# =============
+# - continous interior penalty (cip) with three parameters delta_i
+stabilization:
+  cip:
+    enable: True
+    delta_1: 1.0
+    delta_2: 1.0
+    delta_3: 0.01
+
+# Formulation Parameters
+# ======================
+
+# Number of spatial dimensions, currently only two-dimensional.
+nsd: 2
+
+# heat, stress, coupled
+mode: "stress"
+
+# Coefficients as in westerkamp2019 or without as in torrilhon2017
+use_coeffs: True
+
+# Knudsen number
+tau: 0.08
+
+# Refaction coefficient
+xi_tilde: 1.0
+# xi_tilde: 0.7978845608 # sqrt(2/pi)
+
+bcs:
+  3000:
+    "name": "upper"
+    "theta_w": 1.0
+    "v_t": -1.0
+  3100:
+    "name": "lower"
+    "theta_w": 0.5
+    "v_t": 0.0
+
+# heat source
+heat_source: "2.0 - 1.0 * pow(sqrt(pow(x[0],2)+pow(x[1],2)),2)"
+
+# mass source
+mass_source: "0"
+
+# Perform convergence study on given set of meshes with exact solution
+convergence_study:
+  enable: False
+  exact_solution: esols/01_source_rot.cpp
+  plot: False
+  write_systemmatrix: False

fenicsR13/examples/lid_driven_cavity/lid.geo

+// Command line Parameters
+If(!Exists(p))
+  p = 5;
+EndIf
+
+// Settings
+res = 100;
+Mesh.CharacteristicLengthMax = 1.0 * 2^(-p);
+Mesh.MshFileVersion = 2.0;
+
+Point(1001) = {0, 0, 0, res};
+Point(1002) = {1, 0, 0, res};
+Point(1003) = {1, 1, 0, res};
+Point(1004) = {0, 1, 0, res};
+
+Line(2001) = {1001,1002};
+Line(2002) = {1002,1003};
+Line(2003) = {1003,1004};
+Line(2004) = {1004,1001};
+
+Line Loop(3000) = {2003}; Physical Curve("upper",3000) = {2003};
+Line Loop(3100) = {2004,2001,2002}; Physical Curve("lower",3100) = {2004,2001,2002};
+
+Plane Surface(4000) = {3000,3100}; Physical Surface("mesh",4000) = {4000};