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Staggered schemes for all speed flows. (English) Zbl 1357.76038

Summary: We review in this paper a class of schemes for the numerical simulation of compressible flows. In order to ensure the stability of the discretizations in a wide range of Mach numbers and introduce sufficient decoupling for the numerical resolution, we choose to implement and study pressure correction schemes on staggered meshes. The implicit version of the schemes is also considered for the theoretical study. We give both algorithms for the barotropic Navier-Stokes equations, for the full Navier-Stokes equations and for the Euler equations. In each case, we summarize the theoretical results that were recently obtained concerning the stability and consistency of the schemes and present some numerical results which confirm their good performance.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76Nxx Compressible fluids and gas dynamics
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