multigrid solver in stretched/nonuniform grids?
 

Hi All,

Could you plese share share your experience/knowledge on multigrid solver for poisson equation in strtetched or nonuniform grids? I have succeed in using multigrid (MUDPACK) to solve pressure poisson equation in uniform grids. In order to simulate the near-wall flow, I have to use the stretech grids in the noraml wall direction. The simulation resultis good when using SOR, but it fails in convergence with multigrid. I do appreciate your any advice.

Re: multigrid solver in stretched/nonuniform grids
 

Hi there,

For uniform grid, multigrid works so well that it doesn't really matter what type of smoother you are using. Now, when stretched grids are used, and especially when you have a very high cell aspect ratio, then the choice of an appropriate smoother is of particular interest.

As suggested by Brandt ("Multilevel adaptive solutions to boundary value problems", Math. Comp., vol. 31, pp. 333-390, 1977), when meshes with high aspect ratio are used, especially in the case of viscous flows, the use of a line SOR solver is advocated in order to keep a good convergence rate.

What I have done in my particular case is, I use 3 types of smoother (line SOR in x-dir, line SOR in y-dir and regular point SOR) and alternate their use in the iteration process (use of structured grid).

I hope this helps,

Sincerely,

Frederic Felten.

Re: multigrid solver in stretched/nonuniform grids
 

Hi Frederic,

Thanks very much for your reply.

I'd like to ask you another question. Do you transform the stretched grids in the physics domain to the uniform grids in the computational domain, or use the stretched grids directly in your multigrid solver?

Thanks again.

Lewis

Re: multigrid solver in stretched/nonuniform grids
 

Hi lewis,

I do not transform the stretched grid. I use the multigrid solver in physical space. Actually, if you generate your grid using an eliptic grid generator, and if you make sure that the grid is smooth enough (in my case the stretching ratio between adjacent cell is about 1.05) then it is almost like working with uniform grids.

Now in my case, with a relatively smooth slow varying grid, I am using fixed weights when performing the restriction step and the prolongation step, and it works really well. I have implemented 4 grid levels, and each coaser grid is determined by only retaining 1 out of every 2 points in each directions.

I hope this helps,

Sincerely,

Frederic Felten.