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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.

MSC:
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)
Software:
HE-E1GODF
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