### I have a doubt about slip condition.

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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?

Thanks in advance.

```
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

### 1 Answer

4

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.
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