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On the behavior of upwind schemes in the low Mach number limit. II: Godunov type schemes. (English) Zbl 1049.76040
Summary: This paper presents an analysis of Godunov scheme in the low Mach number regime [for part I see the first author and C. Viozat, ibid. 28, No. 1, 63–86 (1999; Zbl 0963.76062)]. We study the Riemann problem and show that the interface pressure contains acoustic waves of order \(\mathcal O(M_{\ast})\), where \(M_{\ast}\) is the reference Mach number, even if the initial data are well-prepared and contain only pressure fluctuations of order \(\mathcal O(M_{\ast}^2)\). We then propose to modify the fluxes computed by Godunov type schemes by solving a preconditioned Riemann problem instead of the original one. We show that this strategy allows to recover a correct scaling of pressure fluctuations. Numerical experiments confirm these theoretical results.

76M12 Finite volume methods applied to problems in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
Full Text: DOI
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