Numerical Solution of Compressible and Incompressible Flows with Equal Interpolations and Explicit Integration

Abstract

We present a stabilized algorithm for the incompressible or nearly incompressible Navier-Stokes equations, allowing equal order interpolations. The stabilization terms are obtained as a straightforward extension of the SUPG (for Streamline Upwind Petro~'-Galerkin) method to multidimensional advective-diffusive system of equations. We show also how the explicit scheme can be used in the incompressible regime through the use of a specially devised preconditioning. Using this techniques, rates of convergence independent of Mach number are achieved and compressible explicit codes can be used in the incompressible limit.