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A unified time-marching procedure for compressible and incompressible flows. (English) Zbl 0881.76066

Summary: A time derivative preconditioning is introduced that allows a unified treatment of time-marching methods for both compressible and incompressible flows from inviscid to creeping flows. Results show that convergence rates are independent of Reynolds numbers and Mach numbers. A complete formulation based on an arbitrary equation of state facilitates the changes from one type of fluid to another and, in particular, the extension to incompressible flows. The resulting time-marching algorithm is shown in the incompressible limit to be identical with iterative methods based on pressure-Poisson methods, and it is demonstrated that both methods are hyperbolic.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76D99 Incompressible viscous fluids
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