Operator splitting and upwinding for the Navier-Stokes equations

Abstract

We present an operator splitting scheme for the unsteady Navier-Stokes equations for incompressible viscous fluid flow. Like other operator splitting methods applied to these equations, the difficulties associated with the nonlinearity and the incompressibility condition are decoupled. At each time step we obtain two subproblems of Stokes type and a linear one of elliptic type. The linear problem gives us uncoupled scalar problems of transport type; then, we may take advantage of well known upwind techniques for such kind of problems in order to handle large Reynolds numbers flow with coarse meshes. To show the efficiency of the scheme we report numerical results up to Reynolds numbers Re=4000 obtained with very coarse meshes.