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On the behaviour of upwind schemes in the low Mach number limit

Hervé Guillard 1 Cécile Viozat 1 
1 SINUS - Numerical Simulation for the Engineering Sciences
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This paper presents an asymptotic analysis in power of the Mach number of the flux difference splitting approximation of the compressible Euler equations in the low Mach number limit. We prove that the solutions of the discrete system contain pressure fluctuations of order of the Mach number while the continuous pressure scales with the square of the Mach number. This explains in a rigorous manner why this approximation of the compressible equations fails to compute very subsonic flow. We then show that a preconditioning of the numerical dissipation tensor allows to recover a correct scaling of the pressure. These theoretical results are totally confirmed by numerical experiments.
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Submitted on : Thursday, October 10, 2013 - 11:36:22 AM
Last modification on : Friday, February 4, 2022 - 3:24:51 AM

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Hervé Guillard, Cécile Viozat. On the behaviour of upwind schemes in the low Mach number limit. Computers and Fluids, Elsevier, 1999, 28 (1), pp.63-86. ⟨10.1016/S0045-7930(98)00017-6⟩. ⟨hal-00871725⟩



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