On the mixed approximation type pressure correction method for incompressible Navier-Stokes equations

Abstract

In the paper we consider a numerical method for the solution of the Navier– Stokes equations. We perform pressure velocity coupling in the mixed approximation type. We construct the approximation using finite element method for the pressure and finite volume/difference method for velocity variables. WENO scheme is used for velocity advection. The method is stable under common CFL criterion for advection equations. Then we demonstrate the correctness of velocity–pressure coupling for the Stokes flow. Finaly the method is benchmarked against reference analytical and numerical solutions of the Navier– Stokes equations. It is shown that the method has high accuracy and can be used to perform direct numerical simulation of incompressible fluid flow.