Unified formulation for compressible and incompressible flows by using multi-integrated moments II: Multi-dimensional version for compressible and incompressible flows

Following our previous paper on a novel finite volume formulation for computing flows of any Mach number, we present the multi-dimensional extension of the method in this paper. Treating two kinds of averages, which are generically called 'moments' and defined as the volume integrated average (VIA) and the surface integrated average (SIA) in this paper, as the prognostic variables makes the present method different from the conventional finite volume method where only VIA is the basic variable. The resulting discretization approach, which is a type of the CIP/multi-moment finite volume method and called VSIAM3 (volume/surface integrated average-based multi-moment method), is combined with a pressure-based projection formulation for the time integration to enable the simulations for both compressible and incompressible flows. The numerical algorithm for multi-dimensions will be reported in this paper. Numerical experiments with flows of a wide range Mach numbers will be also presented.