Hi, I'm Nailya. I solve Navier-Stokes equations in implicit way using finite difference method on unstructured meshes, TVD method, Newton's method. The obtained linearized system I try to solve using GMRES method. The problem is that the matrix of system is very ill-conditioned. I need in a good preconditioner. How can I obtain it?

You can try to find some packages such as QMRPACK, SPARKSKIT from netlib and there are some preconditioning GMRES built in...

Nailya, Why is your system of equations so ill-conditioned? Make sure you assemble your matrix correctly. You can start trying to precondition your system of equations using a Jacobi Preconditioner.

Chuck