On the Extension of Compressible Flow Solvers to Incompressible Flows

Abstract

An alternative method to low speed preconditioning for the computation of nearly incompressible flows with compressible methods is developed. For this approach the leading terms of the Flux Difference Splitting approximate Riemann solver are analyzed in the incompressible limit. In combination with the requirement of the velocity field to be divergence-free, an elliptic equation to solve for a pressure correction to enforce the divergence-free velocity field on the discrete level is derived. The pressure correction equation established is shown to be equivalent to classical methods for incompressible flows. However, in the derivation presented here, no heuristic arguments are required, but the discrete method arises consistently from the compressible formulation. In order to allow the computation of flows at all speeds, a blending technique for the transition from the incompressible, pressure based formulation to the compressible, density based formulation is established. As a guidance for this blending technique, again the approximate solution of the Riemann problem is used. Compared with standard preconditioning techniques, the pressure correction method developed here showed improved robustness for high lift flows close to separation.