Merkle, Charles L.; Feng, Jin-zhang A unified time-marching procedure for compressible and incompressible flows. (English) Zbl 0881.76066 J. Hydrodyn., Ser. B 7, No. 4, 13-21 (1995). 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 Keywords:hyperbolic method; time derivative preconditioning; creeping flows; convergence; arbitrary equation of state; incompressible limit; iterative methods; pressure-Poisson methods PDFBibTeX XMLCite \textit{C. L. Merkle} and \textit{J.-z. Feng}, J. Hydrodyn., Ser. B 7, No. 4, 13--21 (1995; Zbl 0881.76066)