On the behaviour of upwind schemes in the low Mach number limit. (English) Zbl 0963.76062

Summary: This paper presents an asymptotic analysis (in power of Mach number) of the flux difference splitting approximation of compressible Euler equations in the low Mach number limit. We prove that the solutions of discrete system contain pressure fluctuations of order of Mach number, while the continuous pressure scales with the square of Mach number. This explains in a rigorous manner why this approximation of compressible equations fails to compute subsonic flows. Finally, we show that a preconditioning of numerical dissipation tensor allows to recover a correct scaling of the pressure. These theoretical results are confirmed by numerical experiments.


76M20 Finite difference methods applied to problems in fluid mechanics
76G25 General aerodynamics and subsonic flows
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