Error in setting Boundary Conditions for DFG benchmark 2D-1

I am trying to convert my legacy FEniCS code to FEniCSx. I’m working on the DFG benchmark 2D-1 in FeatFlow (DFG benchmark 2D-1 (RE20, laminar) - Featflow). I am getting several errors while setting up the boundary conditions. I am using the same mesh from the tutorial of the DFG 2D-3 benchmark.

The working legacy FEniCS code is:

# Define boundaries
inflow   = 'near(x[0], 0)'
outflow  = 'near(x[0], 2.2)'
walls    = 'near(x[1], 0) || near(x[1], 0.41)'
cylinder = 'on_boundary && x[0]>0.1 && x[0]<0.3 && x[1]>0.1 && x[1]<0.3'

# Define inflow profile
inflow_profile = ('4.0*0.3*x[1]*(0.41 - x[1]) / pow(0.41, 2)', '0')

# Define boundary conditions
bcu_inflow = DirichletBC(W.sub(0), Expression(inflow_profile, degree=2), inflow)
bcu_walls = DirichletBC(W.sub(0), Constant((0, 0)), walls)
bcu_cylinder = DirichletBC(W.sub(0), Constant((0, 0)), cylinder)
bcp_outflow = DirichletBC(W.sub(1), Constant(0), outflow)
bc = [bcu_inflow, bcu_walls, bcu_cylinder, bcp_outflow]

The FEniCSx code I tried is:

# Reading Mesh 
mesh, cell_tags, facet_tags = read_from_msh("mesh2D.msh", MPI.COMM_WORLD, 0, gdim=2)
fdim = mesh.topology.dim - 1

# Material parameters
nu = fem.Constant(mesh, PETSc.ScalarType(0.001))  # Kinematic viscosity

P2 = ufl.VectorElement("Lagrange", mesh.ufl_cell(), 2)
P1 = ufl.FiniteElement("Lagrange", mesh.ufl_cell(), 1)
V, Q = fem.FunctionSpace(mesh, P2), fem.FunctionSpace(mesh, P1)

# Create the function space
TH = P2 * P1
W = fem.FunctionSpace(mesh, TH)
W0, _ = W.sub(0).collapse()

def velocity_expression(x):
    values = np.zeros((mesh.geometry.dim, x.shape[1]),dtype=PETSc.ScalarType)
    values[0] = 4.0*0.3*x[1]*(0.41 - x[1]) / pow(0.41, 2)
    return values

# Inlet
u_inlet = fem.Function(V)
u_inlet.interpolate(velocity_expression)
bcu_inflow = fem.dirichletbc(u_inlet, fem.locate_dofs_topological((W.sub(0), V), fdim, facet_tags.find(2)), W.sub(0))
# Walls
u_nonslip = np.array((0,) * mesh.geometry.dim, dtype=PETSc.ScalarType)
bcu_walls = fem.dirichletbc(u_nonslip, fem.locate_dofs_topological((W.sub(0), V), fdim, facet_tags.find(4)), W.sub(0))
# Obstacle
bcu_obstacle = fem.dirichletbc(u_nonslip, fem.locate_dofs_topological((W.sub(0), V), fdim, facet_tags.find(5)), W.sub(0))
# Outlet
bcp_outlet = fem.dirichletbc(PETSc.ScalarType(0), fem.locate_dofs_topological((W.sub(1), Q), fdim, facet_tags.find(3)), W.sub(1))

bc = [bcu_inflow, bcu_obstacle, bcu_walls,bcp_outlet]

This produces a considerable error statement:

Traceback (most recent call last):
  File "/Users/varunkumar/opt/anaconda3/envs/fenicsx/lib/python3.10/site-packages/dolfinx/fem/bcs.py", line 125, in __init__
    super().__init__(_value, dofs, V)  # type: ignore
TypeError: __init__(): incompatible constructor arguments. The following argument types are supported:
    1. dolfinx.cpp.fem.DirichletBC_float64(g: numpy.ndarray[numpy.float64], dofs: numpy.ndarray[numpy.int32], V: dolfinx::fem::FunctionSpace)
    2. dolfinx.cpp.fem.DirichletBC_float64(g: dolfinx::fem::Constant<double>, dofs: numpy.ndarray[numpy.int32], V: dolfinx::fem::FunctionSpace)
    3. dolfinx.cpp.fem.DirichletBC_float64(g: dolfinx::fem::Function<double>, dofs: numpy.ndarray[numpy.int32])
    4. dolfinx.cpp.fem.DirichletBC_float64(g: dolfinx::fem::Function<double>, dofs: List[numpy.ndarray[numpy.int32][2]], V: dolfinx::fem::FunctionSpace)

Invoked with: array([0., 0.]), [array([    0,     1,     2,     3,     8,     9,    36,    37,    40,
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During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File "/Users/varunkumar/Downloads/FEniCSx v0.6/DFG2D-1.py", line 37, in <module>
    bcu_walls = fem.dirichletbc(u_nonslip, fem.locate_dofs_topological((W.sub(0), V), fdim, facet_tags.find(4)), W.sub(0))
  File "/Users/varunkumar/opt/anaconda3/envs/fenicsx/lib/python3.10/site-packages/dolfinx/fem/bcs.py", line 183, in dirichletbc
    return formcls(value, dofs, V)
  File "/Users/varunkumar/opt/anaconda3/envs/fenicsx/lib/python3.10/site-packages/dolfinx/fem/bcs.py", line 127, in __init__
    super().__init__(_value, dofs, V._cpp_object)  # type: ignore
TypeError: __init__(): incompatible constructor arguments. The following argument types are supported:
    1. dolfinx.cpp.fem.DirichletBC_float64(g: numpy.ndarray[numpy.float64], dofs: numpy.ndarray[numpy.int32], V: dolfinx::fem::FunctionSpace)
    2. dolfinx.cpp.fem.DirichletBC_float64(g: dolfinx::fem::Constant<double>, dofs: numpy.ndarray[numpy.int32], V: dolfinx::fem::FunctionSpace)
    3. dolfinx.cpp.fem.DirichletBC_float64(g: dolfinx::fem::Function<double>, dofs: numpy.ndarray[numpy.int32])
    4. dolfinx.cpp.fem.DirichletBC_float64(g: dolfinx::fem::Function<double>, dofs: List[numpy.ndarray[numpy.int32][2]], V: dolfinx::fem::FunctionSpace)

Invoked with: array([0., 0.]), [array([    0,     1,     2,     3,     8,     9,    36,    37,    40,
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       13092, 13093, 13096, 13097], dtype=int32)], <dolfinx.cpp.fem.FunctionSpace object at 0x10ef0d7b0>

I can’t figure out what’s wrong with the code. Any help is very much appreciated.

Consider the following (using a random meshtag and mesh as you have not supplied yours:

from dolfinx import fem
from dolfinx.mesh import create_unit_square, meshtags
from mpi4py import MPI
import ufl
from petsc4py import PETSc
import numpy as np
# Reading Mesh
mesh = create_unit_square(MPI.COMM_WORLD, 10, 10)
fdim = mesh.topology.dim - 1
mesh.topology.create_entities(mesh.topology.dim-1)
fl = np.arange(mesh.topology.index_map(mesh.topology.dim-1).size_local, dtype=np.int32)
facet_tags = meshtags(mesh, fdim, fl, fl)

# Material parameters
nu = fem.Constant(mesh, PETSc.ScalarType(0.001))  # Kinematic viscosity

P2 = ufl.VectorElement("Lagrange", mesh.ufl_cell(), 2)
P1 = ufl.FiniteElement("Lagrange", mesh.ufl_cell(), 1)
V, Q = fem.FunctionSpace(mesh, P2), fem.FunctionSpace(mesh, P1)

# Create the function space
TH = P2 * P1
W = fem.FunctionSpace(mesh, TH)
W0, _ = W.sub(0).collapse()


def velocity_expression(x):
    values = np.zeros((mesh.geometry.dim, x.shape[1]), dtype=PETSc.ScalarType)
    values[0] = 4.0*0.3*x[1]*(0.41 - x[1]) / pow(0.41, 2)
    return values


# Inlet
u_inlet = fem.Function(V)
u_inlet.interpolate(velocity_expression)
bcu_inflow = fem.dirichletbc(u_inlet, fem.locate_dofs_topological(
    (W.sub(0), V), fdim, facet_tags.find(2)), W.sub(0))
# Walls
u_nonslip = fem.Function(V)
u_nonslip.x.set(0.)
bcu_walls = fem.dirichletbc(u_nonslip, fem.locate_dofs_topological(
    (W.sub(0), V), fdim, facet_tags.find(4)), W.sub(0))
# Obstacle
bcu_obstacle = fem.dirichletbc(u_nonslip, fem.locate_dofs_topological(
    (W.sub(0), V), fdim, facet_tags.find(5)), W.sub(0))
# Outlet
bcp_outlet = fem.dirichletbc(PETSc.ScalarType(0), fem.locate_dofs_topological(
    W.sub(1), fdim, facet_tags.find(3)), W.sub(1))

bc = [bcu_inflow, bcu_obstacle, bcu_walls, bcp_outlet]