Multigrid on FDM

Enda Bigarelli

Hi.

I hope someone can help me with my master thesis. I am using an explicit, 2nd order, 3-D finite difference algorithm, with central differences. Artificial dissipation is calculated using the scalar Turkel&Vatsa model. This code is used for rocket-like configuration applications. Boundary conditions include: far field, exit, center-line averaging and solid wall 1st-order extrapolation.

This simple wall condition leads to a contact surface near the wall (Chakravarthy says so!), which (I believe so!) impairs the convergence of the code. Thus, I tried to implement a multigrid process into the code. As an FAS method, it starts (from scratch) in the finer grid and sweeps till the coarser, and then back. I've used bilinear interpolation and tested both the direct injection and the full-weighted restriction. However, the code is NOT converging. It is even blowing with the full-weighted restriction.

It seems to spoil the solution at the "normal" shock wave region and at the adjacent nose wall. I don't have any idea why it is acting so. I wonder whether this problem is due to the proximity of the "normal" shock wave to the nose wall, or it is created by the contact surface or any other boundary condition. Does anyone have any idea of what is going wrong with the multigrid and/or the solid wall condition?

I would appreciate very much your help.

Best regards,

Biga