How to define a Slip boundary condition for Navier-Stokes incompressible equations (segregated solver)

Question

Hi,

I want to define a "Slip" boundary condition instead a "Wall' or "No Slip" boundary condition for Navier-Stokes incompressible equations.

I saw an example of Navier-Stokes incompressible equations in the Fenics demo, but I don't undestand how to define the "Slip" condition.

As I undestand the "Slip" boundary condition is:
if scalar: zeroGradient;
if vector: normal component is FixedValue = zero, tangential components are zeroGradient;

Or:
A slip boundary condition corresponds to setting the normal component
of the velocity U * n to zero at the boundary and models a boundary with
neglible friction which the flow cannot penetrate.

link to the Fenics demo example:
http://fenicsproject.org/documentation/dolfin/1.5.0/python/demo/documented/navier-stokes/python/documentation.html

I think I must change the equation for "Tentative velocity step":

F1 = (1/k)*inner(u - u0, v)*dx + inner(grad(u0)*u0, v)*dx + \
     nu*inner(grad(u), grad(v))*dx - inner(f, v)*dx

to:

F1 = (1/k)*inner(u - u0, v)*dx + inner(grad(u0)*u0, v)*dx + \
     nu*inner(grad(u), grad(v))*dx - inner(f, v)*dx -  nu*inner(grad(u) * n, v)*ds[wall boundary number]

The other two equations for "Pressure update" and "Velocity update" are remain unchanged.

Also I have to change

bcu = [noslip]
bcp = [inflow, outflow]

to

bcu = []
bcp = [inflow, outflow]

Am I right?

Thanks in advance!

Regards,
Maksim

Comments

Hi Maks,

Did you have any success with this? It looks correct to me, although you might have to scale the added term with a constant to enforce the boundary condition stronger.

---

Hi Øyvind Evju,

Firstly, excuse me for long answer.

No, it doesn't work.

I think you need to put strong slip boundary condition for velocity, but it doesn't implemented in fenics dolfin, that is u_n = 0 on the corecpondent boundary.

I found some interesting information about this in the followind article "Adaptive Algorithms and High Order Stabilization for Finite Element Computation of Turbulent Compressible Flow, MURTAZO NAZAROV, Doctoral Thesis, Stockholm, Sweden 2011".

The slip boundary condition also has been implemented in the unicorn solver, but the unicorn is too old and the latest version support only dolfin-0.8.2-hpc.

Thanks in advance!

Link to unicorn: https://launchpad.net/unicorn