Answer to stackoverflow question, https://stackoverflow.com/questions/58695069/fipy-convection-with-a-given-velocity-field

tmp.py

from fipy import Grid2D, CellVariable, FaceVariable
from fipy import ConvectionTerm, DiffusionTerm, TransientTerm
import numpy as np
from scipy import interpolate
from fipy import LinearGMRESSolver

dx = 0.5
nx = 7
dy = 0.5
ny = 7

xy = np.zeros((nx, ny, 2))
xy[:, :,  0] = np.mgrid[0:nx, 0:ny][0] * dx
xy[:, :, 1] = np.mgrid[0:nx, 0:ny][1] * dy

u = xy[..., 0] + xy[..., 1]
v = xy[..., 0] * xy[..., 1]

print(xy.shape)
print(u.shape)
print(v.shape)
m = Grid2D(nx=3, ny=3, dx=1.0, dy=1.0)

xy_interp = np.array(m.faceCenters).swapaxes(0, 1)
u_interp = interpolate.griddata(xy.reshape(-1, 2), u.flatten(), xy_interp, method='cubic')
v_interp = interpolate.griddata(xy.reshape(-1, 2), v.flatten(), xy_interp, method='cubic')

var = CellVariable(mesh=m)

diffusion = 1.0
velocity = FaceVariable(mesh=m, rank=1)

print(u_interp)
print(v_interp)
velocity[0, :] = u_interp
velocity[1, :] = v_interp


eqn = TransientTerm() + ConvectionTerm(velocity) == DiffusionTerm(diffusion)


eqn.solve(var, dt=1.0)

Thanks for the example, but the solution I get is just zeros..