Analysis of Godunov type schemes applied to the compressible Euler system at low Mach number
摘要：
We propose a theoretical framework to clearly explain the inaccuracy of Godunov type schemes applied to the compressible Euler system at low Mach number on a Cartesian mesh. In particular, we clearly explain why this inaccuracy problem concerns the 2D or 3D geometry and does not concern the 1D geometry. The theoretical arguments are based on the Hodge decomposition, on the fact that an appropriate well-prepared subspace is invariant for the linear wave equation and on the notion of first-order modified equation. This theoretical approach allows to propose a simple modification that can be applied to any colocated scheme of Godunov type or not in order to define a large class of colocated schemes accurate at low Mach number on any mesh. It also allows to justify colocated schemes that are accurate at low Mach number as, for example, the Roe–Turkel and the AUSM +-up schemes, and to find a link with a colocated incompressible scheme stabilized with a Brezzi–Pitkranta type stabilization. Numerical results justify the theoretical arguments proposed in this paper.
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关键词：
Theoretical or Mathematical/ compressible flow finite volume methods Navier-Stokes equations/ Godunov type schemes compressible Euler system low Mach number Hodge decomposition linear wave equation/ A4710 General fluid dynamics theory, simulation and other computational methods
DOI：
10.1016/j.jcp.2009.09.044
被引量：
年份：
2010
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