A Matrix-Free Preconditioner Applied to CFD

Overview & Synopsis

We consider the implicit time integration of the compressible Navier-Stokes equations. Each implicit step involves the solution of a costly non linear system. In this paper, we define a preconditioner to solve each linear system more cheaply within the framework of matrix-free algorithm. The main idea is to reuse the Krylov subspace across the time steps. We demonstrate some properties of the preconditioner and show the practical value of this approach for stiff problems which needs excessive small time steps with an explicit method.