3
$\begingroup$

please can you help me with my problem with Stokes flow written using Marker and cell method (MAC)? I need only to solve the eq. of continuity + momentum eq. for a given condition (steady state). I don't understand how to do the things on boundaries (lets say I want to have v=0 on boundaries), how to fill the matrix - I will solve it as Ax=b where A is matrix 3*N*Nx3*N*N and b right hand side vector of dim 3*N*N if my box is NxN and I have 3 unknowns (vx,vy,p) and three eq. ( eq. of continuity + 2 momentum eq.) Or is there any code I can have a look at to get a flavor of it? Many thanks

$\endgroup$
1
3
$\begingroup$

The original publications by Harlow and Welch discusses this. If you search for "Harlow Welch marker cell" in your favorite search engine, you should get a few links to copies. If this does not help, my own article in Int. J. Num. Meth. Fluids titled "Divergence-free discontinuous Galerkin schemes for the Stokes equations and the MAC scheme", available in preprint version at http://www.isc.tamu.edu/publications-reports/tr/0705.pdf may help.

For the condition u dot n = f, you set the degrees of freedom on the boundary to the values of f.

For the condition on the tangential velocity, you apply a penalty formulation, which can for instance be reduced to additional terms of the form alpha (u-f) = 0 for all degrees of freedom which are on edges originating from the boundary, but not subset of the boundary.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.