Dirichletbc not working as expected for slip condition

dolfinx
1

Hi Community,

As desribed in this post:

which is exactly the case for my problem. Since I have a long MWE solving a stokes equations with some geometries (which I included in another post and have flagged for deletion), can someone check if I am applying the BC at the subspace properly given how I defined the problem:

P2 = element("Lagrange", msh.basix_cell(), 2, shape=(msh.geometry.dim,))
P1 = element("Lagrange", msh.basix_cell(), 1)

# Create the Taylor-Hood function space
TH = mixed_element([P2, P1])
W = functionspace(msh, TH)
V, _ = W.sub(0).collapse()
# perfect slip bc
slip = Function(V)
dofs_slip = locate_dofs_topological((W.sub(0), V), 1, facet_tag.find(4))
bc_slip = dirichletbc(slip,dofs_slip,W.sub(0).sub(1))

because dirichletbc still seems to be prescribing a noslip condition even if I specified W.sub(0).sub(1) (I want no velocity in y-direction).
If this is the correct way to do it, then I know I must have done something else wrong.

2

The following works for me

import basix.ufl
import dolfinx
import dolfinx.fem
import dolfinx.io
import dolfinx.mesh
import mpi4py.MPI
import numpy as np

# Create mesh
mesh = dolfinx.mesh.create_rectangle(
    mpi4py.MPI.COMM_WORLD, [np.array([0.0, 0.0]), np.array([1.0, 1.0])], [10, 10], dolfinx.mesh.CellType.triangle)

# Mark a boundary
left_boundary_entities = dolfinx.mesh.locate_entities_boundary(
    mesh, mesh.topology.dim - 1, lambda x: np.isclose(x[0], 0.0))


# Create the Taylor-Hood function space
P2 = basix.ufl.element("Lagrange", mesh.basix_cell(), 2, shape=(mesh.geometry.dim,))
P1 = basix.ufl.element("Lagrange", mesh.basix_cell(), 1)
TH = basix.ufl.mixed_element([P2, P1])
W = dolfinx.fem.functionspace(mesh, TH)

# Assign BC on the second component of the velocity space
V, _ = W.sub(0).collapse()
V1, _ = V.sub(1).collapse()
bc_value = dolfinx.fem.Function(V1)
bc_value.interpolate(lambda x: 1 + x[1])
left_boundary_dofs = dolfinx.fem.locate_dofs_topological(
    (W.sub(0).sub(1), V1), mesh.topology.dim - 1, left_boundary_entities)
bc = dolfinx.fem.dirichletbc(bc_value, left_boundary_dofs, W.sub(0).sub(1))

# Apply BC
solution = dolfinx.fem.Function(W)
dolfinx.fem.set_bc(solution.x.array, [bc])

# Export for visualization
with dolfinx.io.VTXWriter(mesh.comm, "velocity.bp", solution.sub(0).collapse()) as vtx_file:
    vtx_file.write(0.0)

with dolfinx.io.VTXWriter(mesh.comm, "pressure.bp", solution.sub(1).collapse()) as vtx_file:
    vtx_file.write(0.0)
3

Thanks, it works perfectly now!