A Flux-Splitting Scheme for Compressible and Incompressible Flows

In the present work, a recently proposed flux-splitting scheme suitable for compressible flow is extended to incompressible flows. Appropriate dissipation terms for both incompressible and compressible flows are determined by expanding the Roe flux-difference splitting in terms of Mach number. Analysis of the dissipation terms in this form for both the Roe scheme and the basic (current) scheme leads to the incorporation of certain terms into the basic scheme to establish the transition from compressible flow toward the incompressible limit. Using the proper terms in the dissipation formulation, convergence rates for airfoil flows became nearly independent of the freestream Mach number.