### I have a doubt about slip condition.

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6 months ago by

I have been testing some ways to implement slip boundary condition. One way that I have in mind is Nitsche's method, but now I am wondering if I can simply prescribe zero the normal component $v_{y} =0$ and let the tangent one free  $v_{x}$ instead of use Nitsche's method. So, is FEniCS able to give a good result if I do following implementation?

from dolfin import *
import mshr

# Build function spaces (Taylor-Hood)
V = VectorElement("Lagrange", mesh.ufl_cell(), 2)
P = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
W0 = MixedElement([V,P])
W = FunctionSpace(mesh,W0)

# slip boundary condition for velocity on walls and

noslip = Constant(0)

bc_walls = DirichletBC(W.sub(0).sub(1), noslip)

Community: FEniCS Project

This is applicable for simple meshes where you know the outer normal. In such cases you can translate  $v\cdot n=0$v·n=0 into a 0-Dirichlet boundary condition for one component of the velocity. If you have more complex geometries afaik this is not possible in a straightforward way.