Impose Velocity Profile on Inlet Face using Array

2

Is the velocity profile going to vary both in space and time (is it constant per time step?). If it is constant per time step, I do not see your issue. If it is varying in time, is the data points ordered from lowest y-value to highest y-value, and is the number of data points in the numpy array one to one with the number of dofs in the function space?

If so, you could do the following:

from dolfin import *
import numpy as np
mesh = UnitSquareMesh(4,4)

V = VectorFunctionSpace(mesh, "CG", 2)
u_inlet = Function(V)

# As we have a four cells along each side,
# we have 9 degrees of freedom in a "CG-2" space along the left side
values_x = np.array([0.1,0.3,0.5,0.8,1.1,0.8,0.7,0.3,0.2])
values_y = np.zeros(9)
dof_coords = V.tabulate_dof_coordinates()

# Identify coordinates where x[0]=0
dofs_on_left_side = np.flatnonzero(np.isclose(dof_coords[:,0], 0))
left_dofs_coords = dof_coords[dofs_on_left_side]
#Sort these coord by increasing y-coordinate
sorted_indices = np.argsort(left_dofs_coords[:,1])

# From the sorted dofs, decide which is the x and y component of the space
x_dofs = V.sub(0).dofmap().dofs()
y_dofs = V.sub(1).dofmap().dofs()
x_c, y_c = 0, 0
for index in sorted_indices:
    dof = dofs_on_left_side[index]
    if dof in x_dofs:
        u_inlet.vector().vec().setValueLocal(dof, values_x[x_c])
        x_c +=1
    elif dof in y_dofs:
        u_inlet.vector().vec().setValueLocal(dof, values_y[y_c])
        y_c +=1
XDMFFile("u_inlet.xdmf").write_checkpoint(u_inlet, "u", 0)

And repeat this insertion into u_inlet once per time step (which you can have assigned to a boundary condition).

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