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Asymptotic Expansions and Numerical Methods for Compressible and Low Mach Number Fluid Flow
Author(s) -
Meister A.
Publication year - 2002
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/1617-7061(200203)1:1<526::aid-pamm526>3.0.co;2-3
Subject(s) - mach number , inviscid flow , euler equations , compressible flow , compressibility , mathematics , context (archaeology) , flow (mathematics) , asymptotic analysis , euler's formula , finite volume method , mach wave , mathematical analysis , classical mechanics , physics , mechanics , geometry , paleontology , biology
The results of a formal asymptotic low Mach number analysis [5, 6] of the Euler equations of gas dynamics are used to extend the validity of a numerical method from the simulation of compressible inviscid flow fields to the low Mach number regime. Although, different strategies are applicable [7, 8, 5, 9] in this context we focus our view to a preconditioning technique recently proposed by Guillard and Viozat [16]. We present a finite volume approximation of the governing equations using a Lax‐Friedrichs scheme whereby a preconditioning of the incorporated numerical dissipation is employed. A discrete asymptotic analysis proves the validity of the scheme in the low Mach number regime.