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On the behavior of upwind schemes in the low Mach number limit: II. Godunov type schemes

✍ Scribed by Hervé Guillard; Angelo Murrone

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
413 KB
Volume
33
Category
Article
ISSN
0045-7930

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✦ Synopsis

This paper presents an analysis of Godunov scheme in the low Mach number regime. We study the Riemann problem and show that the interface pressure contains acoustic waves of order OðM Ã Þ where M Ã is the reference Mach number even if the initial data are well-prepared and contain only pressure fluctuations of order OðM 2 Ã Þ. 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 the pressure fluctuations. Numerical experiments confirm these theoretical results.

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