Compressible and incompressible flow; an algorithm for all seasons

Abstract A semi-implicit algorithm is presented which allows the solution of both incompressible and compressible flows to be achieved in a single code. Both transient and steady state solutions are available and compressibility no longer dictates the time step limits. Difficulties of compressible flow with uniform interpolation which exist due to local incompressibility in low velocity regions are avoided. The transition to the fully explicit form at high Mach number flows can be accomplished automatically yielding a form slightly different from that of conventional procedures. The algorithm is available for shallow water equations where its advantages promise to be large. Several examples illustrate the paper.

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