An Asymptotic-Preserving all-speed scheme for the Euler and Navier-Stokes equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:231

Article

Cordier, Floraine^2,3  Degond, Pierre^1,3  Kumbaro, Anela² 

[1] Univ Toulouse 3, CNRS, Inst Math Toulouse, UMR 5219, F-31062 Toulouse, France

[2] CEA Saclay DEN, DM2S, STMF, LMEC, F-91191 Gif Sur Yvette, France

[3] Univ Toulouse, UPS, INSA, UT1,UTM,Inst Math Toulouse, F-31062 Toulouse, France

关键词: Low Mach number limit;    Asymptotic-Preserving;    All-speed;    Compressible flows;    Incompressible flows;    Navier-Stokes equations;    Euler equations;   

DOI  :  10.1016/j.jcp.2012.04.025

来源: Elsevier

【 摘 要 】

We present an Asymptotic-Preserving 'all-speed' scheme for the simulation of compressible flows valid at all Mach-numbers ranging from very small to order unity. The scheme is based on a semi-implicit discretization which treats the acoustic part implicitly and the convective and diffusive parts explicitly. This discretization, which is the key to the Asymptotic-Preserving property, provides a consistent approximation of both the hyperbolic compressible regime and the elliptic incompressible regime. The divergence-free condition on the velocity in the incompressible regime is respected, and an the pressure is computed via an elliptic equation resulting from a suitable combination of the momentum and energy equations. The implicit treatment of the acoustic part allows the time-step to be independent of the Mach number. The scheme is conservative and applies to steady or unsteady flows and to general equations of state. One and two-dimensional numerical results provide a validation of the Asymptotic-Preserving 'all-speed' properties. (C) 2012 Elsevier Inc. All rights reserved.

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