Pseudo-compressibility methods for the incompressible flow equations

We consider preconditioning methods to accelerate convergence to a steady state for the incompressible fluid dynamic equations. The analysis relies on the inviscid equations. The preconditioning consists of a matrix multiplying the time derivatives. Thus the steady state of the preconditioned system is the same as the steady state of the original system. We compare our method to other types of pseudocompressibility. For finite difference methods preconditioning can change and improve the steady state solutions. An application to viscous flow around a cascade with a non-periodic mesh is presented.