nate
March 6, 2024, 3:42pm
12
Poisseuille flow in a pipe or annulus is typically good for a convergence check since the analytical solutions do not belong to a polynomial space.
If R1 is the inner cylinder radii and R2 is the outer cylinder radii, with constant applied pressure gradient between the two ends G = −dp/dx, the velocity distribution and the volume flux through the annular pipe are
and the code developed by @kamilova-maths
Turns out my maths was wrong, which is unfortunate. I have fixed it, so if anyone has a similar issue, this is the working code:
from dolfin import *
import numpy as np
# Define mesh and geometry - We solve for half of the domain we need, and impose symmetry
mesh = RectangleMesh(Point(0, 0), Point(1, 1), 100, 100)
n = FacetNormal(mesh)
# Define Taylor--Hood function space W
V = VectorElement("CG", triangle, 2)
Q = FiniteElement("CG", triangle, 1)
W = FunctionSpace(mesh, MixedElement([V, Q]))
…
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