Multigrid method for Lax-Wendroff scheme
 

Hi everyone,

I am working with an in-house compressible Navier-Stokes solver which uses the one-step second order Ni's lax-Wendroff scheme.

For accelerating the convergence, I am trying to implement the multigrid in the solver. Actually, in Lax-Wendroff method, because of the coupled descreatization of time and space, the algorithm is a little bit different from explicit multistage codes. It is actually called "multiple-grid" in Ni's first paper.

I just wanted to find out whether anybody have any experience or information about it because it does not seem to be working in my code.

I know this topic has been closed almost 30 years ago and that makes it even more difficult because I can not find anybody alive in the authors to contact.

Thanks.

You can write you discretization in semi-discrete form (discretize only over space, not time). This is greatly preferable from a software perspective since you can use any SSP method for the forward integrator, and can naturally solve for steady states. Once you have a semi-discrete form, you can use pseudotransient continuation (http://www.cs.odu.edu/~keyes/papers/ptc03.pdf) in Newton-Krylov or nonlinear multigrid form to solve for steady state.