multigrid

sureshkumar

Hi sir,

Please spend sometime for me….Myself Sureshkumar doing M.tech in IIT-india. I am doing project on multigrid method…..i am solving 2D lid driven cavity problem with collocated finite volume method(SIMPLE algorithm) approach with Full approximation scheme of multigrid method. I got the results for multigrid 2 level and almost reduction to 40% time that has taken by single grid but I was not getting solution for multigrid 3 level which will take very less time. So I am telling a procedure of multigrid 2 level in a brief manner that what I had done ,so help me how to extend it for 3 level. I am following Peric's paper"Finite volume multigrid prediction of laminar natural convection:bench mark solutions",IJNMF,1990.

v-cycle multigrid 2 level:

1. solving u,v, pressure correction equations on finegrid for some global iterations in the same procedure of finite volume SIMPLE algorithm procedure.

2. Then calculate residuals of u and v and transfer these restricted residuals to coarse grid added as a extra source term, and also restricted u and v values to coarse grid.

3. The main thing is transferring mass fluxes from fine to coarse grid i.e. the initial mass fluxes are conservatively evaluated by summing the fine grid mass fluxes through the corresponding control volume faces. And these coarse grid mass fluxes are only be corrected in the course of coarse grid iterations.

4. On coarse grid ,solving u, v, pressure correction equations for some global iterations to calculate corrections to finegrid u ,v and p_dash values.

5. Then prolongated these variables to fine grid and same v-cycle procedure is repeated.

Doubts regarding v-cycle multigrid 3-level:

upto third level I followed the same procedure of 2-level but when we prolongated u,v and p_dash from very coarse level to medium coarse level what must I have to take care, mainly how to take mass fluxes for intial iteration of medium coarse grid.

Can u tell where I was doing wrong…..and if possible explain in a brief manner how to come from very coarse to medium coarse followed by finegrid………please help me in this regard……….i am waiting for ur reply………..

Thanking u in advance