Trying to disguise sphere with the Navier-Stokes equations

good day
I have tried to reproduce the results of [1], but I get the following error:

TypeError                                 Traceback (most recent call last)
File /usr/local/dolfinx-real/lib/python3.10/dist-packages/dolfinx/fem/function.py:492, in Function.interpolate(self, u, cells, cell_map, expr_mesh, nmm_interpolation_data)
    490 try:
    491     # u is a Function or Expression (or pointer to one)
--> 492     _interpolate(u, cells)
    493 except TypeError:
    494     # u is callable

File /usr/lib/python3.10/functools.py:889, in singledispatch.<locals>.wrapper(*args, **kw)
    886     raise TypeError(f'{funcname} requires at least '
    887                     '1 positional argument')
--> 889 return dispatch(args[0].__class__)(*args, **kw)

File /usr/local/dolfinx-real/lib/python3.10/dist-packages/dolfinx/fem/function.py:455, in Function.interpolate.<locals>._interpolate(u, cells)
    454 """Interpolate a cpp.fem.Function"""
--> 455 self._cpp_object.interpolate(u, cells, nmm_interpolation_data)

TypeError: interpolate(): incompatible function arguments. The following argument types are supported:
    1. interpolate(self, f: ndarray[dtype=float64, writable=False, shape=(*), order='C'], cells: ndarray[dtype=int32, writable=False, shape=(*), order='C']) -> None
    2. interpolate(self, f: ndarray[dtype=float64, writable=False, shape=(*, *), order='C'], cells: ndarray[dtype=int32, writable=False, shape=(*), order='C']) -> None
    3. interpolate(self, u: dolfinx.cpp.fem.Function_float64, cells: ndarray[dtype=int32, writable=False, shape=(*), order='C'], cell_map: ndarray[dtype=int32, writable=False, shape=(*), order='C'], nmm_interpolation_data: tuple[ndarray[dtype=int32, writable=False, shape=(*), order='C'], ndarray[dtype=int32, writable=False, shape=(*), order='C'], ndarray[dtype=float64, writable=False, shape=(*), order='C'], ndarray[dtype=int32, writable=False, shape=(*), order='C']]) -> None
    4. interpolate(self, expr: dolfinx.cpp.fem.Expression_float64, cells: ndarray[dtype=int32, writable=False, order='C'], expr_mesh: dolfinx.cpp.mesh.Mesh_float64, cell_map: ndarray[dtype=int32, writable=False, order='C']) -> None

Invoked with types: dolfinx.cpp.fem.Function_float64, function, ndarray, dolfinx.fem.function.PointOwnershipData

During handling of the above exception, another exception occurred:

RuntimeError                              Traceback (most recent call last)
Cell In[13], line 60
     57     return values
     59 u_in = fem.Function(V)
---> 60 u_in.interpolate(inflow_profile)
     62 u_zero = fem.Function(V)
     63 u_zero.x.array[:] = 0

File /usr/local/dolfinx-real/lib/python3.10/dist-packages/dolfinx/fem/function.py:497, in Function.interpolate(self, u, cells, cell_map, expr_mesh, nmm_interpolation_data)
    495 assert callable(u)
    496 x = _cpp.fem.interpolation_coords(self._V.element, self._V.mesh.geometry, cells)
--> 497 self._cpp_object.interpolate(np.asarray(u(x), dtype=self.dtype), cells)

RuntimeError: Interpolation data has the wrong shape/size.

I have tried to update the code with the new updates and this is the error I continue to have. I attach the updated code:

import dolfinx
import numpy as np
from mpi4py import MPI
from dolfinx.cpp.mesh import CellType
from dolfinx.io import (XDMFFile)
from dolfinx.fem import (Constant, DirichletBC, Function, FunctionSpace, apply_lifting, assemble_matrix, 
                         assemble_scalar, assemble_vector, create_vector, locate_dofs_topological, set_bc)
from petsc4py import PETSc
from ufl import (FacetNormal, Identity, Measure, TestFunction, TrialFunction,
                 as_vector, div, dot, ds, dx, inner, lhs, grad, nabla_grad, rhs, sym)
print(f"DOLFINx version: {dolfinx.__version__} is installed")

filename="sphere-4.xdmf"
with dolfinx.io.XDMFFile(MPI.COMM_WORLD, "sphere-4.xdmf", "r") as xdmf:
       mesh = xdmf.read_mesh(name="Grid")


#### local mesh ####
## mesh = UnitCubeMesh(MPI.COMM_WORLD, 10, 10, 10)
###################

t = 0.00
T = 1. #8                    # Final time
dt = 1./1600.                # Time step size
num_steps = int(T/dt)
k = Constant(mesh, dt)        
mu = Constant(mesh, 0.001)  # Dynamic viscosity
rho = Constant(mesh, 0.5)     # Density

import dolfinx.fem as fem
Q = fem.functionspace(mesh, ("CG", 1))

eps=1e-14

def Inflow(x):
    return np.abs(x[0] - 0.) < eps

def Outflow(x):
    return np.abs(x[0] - 10.0) < eps

def Walls(x):
    result = np.logical_or(np.abs(x[1] + 0.) < eps, np.abs(x[1] - 5.) < eps)
    result2 = np.logical_or(np.abs(x[2] - 0.) < eps, np.abs(x[2] - 5.) < eps)
    return np.logical_or(result, result2)

def Sphere(x):
    result = np.logical_and(x[0] > 2.0 - eps, x[0] < 4.0 + eps)
    result2 = np.logical_and(x[1] > 2.0 - eps, x[1] < 4.0 + eps)
    result3 = np.logical_and(x[2] > 2.0 - eps, x[2] < 4.0 + eps)
    return np.logical_and(np.logical_and(result, result2), result3)

def inflow_profile(x):
    values = np.zeros((3, x.shape[1]), dtype=PETSc.ScalarType)
    values[0, :] = 1.0
    return values

#def inflow_profile(x):
#    values = np.zeros(x.shape)
#    values[0,:]=1
#    return values
V = fem.functionspace(mesh, ("CG", 2))

u_in = fem.Function(V)
u_in.interpolate(inflow_profile)

u_zero = fem.Function(V)
u_zero.x.array[:] = 0
p_zero = fem.Function(Q)
p_zero.x.array[:] = 0

print("Forma de x:", x.shape)
print("Forma de valores:", values.shape)

inflow_boundary_dofs = fem.locate_dofs_geometrical(V, Inflow)
outflow_boundary_dofs = fem.locate_dofs_geometrical(Q, Outflow)
walls_boundary_dofs = fem.locate_dofs_geometrical(V, Walls)
sphere_boundary_dofs = fem.locate_dofs_geometrical(V, Sphere)

bcu_inflow = fem.DirichletBC(u_in, inflow_boundary_dofs)
bcp_outflow = fem.DirichletBC(p_zero, outflow_boundary_dofs)
bcu_walls = fem.DirichletBC(u_zero, walls_boundary_dofs)
bcu_sphere = fem.DirichletBC(u_zero, sphere_boundary_dofs)

bcu = [bcu_inflow, bcu_walls, bcu_sphere]
bcp = [bcp_outflow]

print(f"DOLFINx version: {dolfinx.__version__} is installed")

# Define trial and test functions
u = TrialFunction(V)
v = TestFunction(V)
p = TrialFunction(Q)
q = TestFunction(Q)

# Define functions for solutions at previous and current time steps
u_n = Function(V)
u_ = Function(V)
p_n = Function(Q)
p_ = Function(Q)

# Define expressions used in variational forms
U = 0.5 * (u_n + u)
n = FacetNormal(mesh)
f = Constant(mesh, PETSc.ScalarType((0,0,0)))
k = Constant(mesh, PETSc.ScalarType(dt))
mu = Constant(mesh, PETSc.ScalarType(.001))
rho = Constant(mesh, PETSc.ScalarType(1))

# Define symmetric gradient
def epsilon(u):
    return sym(nabla_grad(u))


# Define stress tensor
def sigma(u, p):
    return 2 * mu * epsilon(u) - p * Identity(len(u))


# Define variational problem for step 1
F1 = rho * dot((u - u_n) / k, v) * dx \
     + rho * dot(dot(u_n, nabla_grad(u_n)), v) * dx \
     + inner(sigma(U, p_n), epsilon(v)) * dx \
     + dot(p_n * n, v) * ds - dot(mu * nabla_grad(U) * n, v) * ds \
     - dot(f, v) * dx
a1 = lhs(F1)
L1 = rhs(F1)

# Define variational problem for step 2
a2 = dot(nabla_grad(p), nabla_grad(q)) * dx
L2 = dot(nabla_grad(p_n), nabla_grad(q)) * dx - (1 / k) * div(u_) * q * dx

# Define variational problem for step 3
a3 = dot(u, v) * dx
L3 = dot(u_, v) * dx - k * dot(nabla_grad(p_ - p_n), v) * dx

# Assemble matrices
#A1 = assemble(a1)
#A2 = assemble(a2)
#A3 = assemble(a3)
A1 = assemble_matrix(a1, bcs=bcu)
A1.assemble()
b1 = create_vector(L1)


A2 = assemble_matrix(a2, bcs=bcp)
A2.assemble()
b2 = create_vector(L2)


A3 = assemble_matrix(a3)
A3.assemble()
b3 = create_vector(L3)



print(f"DOLFINx version: {dolfinx.__version__} is installed")



# Solver for step 1
solver1 = PETSc.KSP().create(MPI.COMM_WORLD)
solver1.setOperators(A1)
solver1.setType(PETSc.KSP.Type.BCGS)
pc1 = solver1.getPC()
pc1.setType(PETSc.PC.Type.JACOBI)

# Solver for step 2
solver2 = PETSc.KSP().create(MPI.COMM_WORLD)
solver2.setOperators(A2)
solver2.setType(PETSc.KSP.Type.MINRES)
pc2 = solver2.getPC()
pc2.setType(PETSc.PC.Type.HYPRE)
pc2.setHYPREType("boomeramg")

# Solver for step 3
solver3 = PETSc.KSP().create(MPI.COMM_WORLD)
solver3.setOperators(A3)
solver3.setType(PETSc.KSP.Type.CG)
pc3 = solver3.getPC()
pc3.setType(PETSc.PC.Type.SOR)


print(f"DOLFINx version: {dolfinx.__version__} is installed")

import dolfinx.io
xdmf = dolfinx.io.XDMFFile(MPI.COMM_WORLD, "solution-4.xdmf", "w")
xdmf.write_mesh(mesh)
xdmf.write_function(u_n, t)
xdmf.write_function(p_n, t)

for i in range(num_steps):
    # Update current time step
    t += dt

    # Step 1: Tentative veolcity step
    with b1.localForm() as loc_1:
        loc_1.set(0)
    assemble_vector(b1, L1)
    apply_lifting(b1, [a1], [bcu])
    b1.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
    set_bc(b1, bcu)
    solver1.solve(b1, u_.vector)
    u_.x.scatter_forward()
    
    # Step 2: Pressure corrrection step
    with b2.localForm() as loc_2:
        loc_2.set(0)
    assemble_vector(b2, L2)
    apply_lifting(b2, [a2], [bcp])
    b2.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
    set_bc(b2, bcp)
    solver2.solve(b2, p_.vector)
    p_.x.scatter_forward()

    # Step 3: Velocity correction step
    with b3.localForm() as loc_3:
        loc_3.set(0)
    assemble_vector(b3, L3)
    b3.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
    solver3.solve(b3, u_.vector)
    u_.x.scatter_forward()

    # Update variable with solution form this time step
    u_n.x.array[:] = u_.x.array[:]
    p_n.x.array[:] = p_.x.array[:]

    # Write solutions to file
    xdmf.write_function(u_n, t)
    xdmf.write_function(p_n, t)

# Close xmdf file
xdmf.close()

Can you help me with this error, please, I have already tried several solutions but none have worked. Also, I attach files from the old version with .h5 and .xdmf files [2]
DOLFINx version: 0.8.0 is installed

The issue is in defining the function space, as you are here defining a second order scalar element, while you want a vector element:

V = fem.functionspace(mesh, ("CG", 2, (mesh.geometry.dim, )))

u_in = fem.Function(V)
u_in.interpolate(inflow_profile)

Please also note that you need to change

to

bcu_inflow = fem.dirichletbc(u_in, inflow_boundary_dofs)
bcp_outflow = fem.dirichletbc(p_zero, outflow_boundary_dofs)
bcu_walls = fem.dirichletbc(u_zero, walls_boundary_dofs)
bcu_sphere = fem.dirichletbc(u_zero, sphere_boundary_dofs)

and

to



# Define variational problem for step 1
F1 = rho * dot((u - u_n) / k, v) * dx \
     + rho * dot(dot(u_n, nabla_grad(u_n)), v) * dx \
     + inner(sigma(U, p_n), epsilon(v)) * dx \
     + dot(p_n * n, v) * ds - dot(mu * nabla_grad(U) * n, v) * ds \
     - dot(f, v) * dx
a1 = dolfinx.fem.form(lhs(F1))
L1 = dolfinx.fem.form(rhs(F1))

# Define variational problem for step 2
a2 = dolfinx.fem.form(dot(nabla_grad(p), nabla_grad(q)) * dx)
L2 = dolfinx.fem.form(dot(nabla_grad(p_n), nabla_grad(q)) * dx - (1 / k) * div(u_) * q * dx)

# Define variational problem for step 3
a3 = dolfinx.fem.form(dot(u, v) * dx)
L3 = dolfinx.fem.form(dot(u_, v) * dx - k * dot(nabla_grad(p_ - p_n), v) * dx)

I would also change the imports

to

from dolfinx.fem import (Constant, Function, )
from dolfinx.fem.petsc import (apply_lifting, assemble_matrix, set_bc, assemble_vector, create_vector)

You should also change the outputting to VTXWriter.
Please note that an up to date splitting scheme for DOLFINx is available at: Test problem 2: Flow past a cylinder (DFG 2D-3 benchmark) — FEniCSx tutorial

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