Multigrid or Krylov subspace for poisson eqn
 

Hi,

I am currently solving my poisson eqn from my FVM fractional step scheme using the Krylov subspace solver. On some high-aspect ratio grids, convergence is slow and it sometimes fails.

My poisson eqn is formed from c-grid of an airfoil. Hence is the multigrid method a better way to solve? Or it depends solely on the actual solver itself?

Thanks

Re: Multigrid or Krylov subspace for poisson eqn
 

1) In general Multi-grid methods are more robust for damping high frequency modes of error, it is attractive when we have fine grid or large number of grids in computational domain. Also as your grid (C-type) is structured, the FAS (multi-grid with full appriximation method) is probably better choice and more easy to implement.

2) But, as you stated that your problem is related to high aspect ratio, not grid refinement, i think one probable source of convergence rate decay (or oscilation) is decreasing accuracy and enlarging truncation error due to large aspect ratio (generally large aspect ration is not suitable). So i recommend using double precision arithmatice (if you use SP) and application of high order methods (specially compact method).