Analysis of an asymptotic preserving low mach number accurate IMEX-RK scheme for the wave equation system

In this paper the analysis of an asymptotic preserving (AP) IMEX-RK finite volume scheme for the wave equation system in the zero Mach number limit is presented. An IMEX-RK methodology is employed to obtain a time semi-discrete scheme, and a space-time fully-discrete scheme is derived by using stand...

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Bibliographic Details
Published in:Applied mathematics and computation 2021-12, Vol.411, p.126469, Article 126469
Main Authors: Arun, K.R., Das Gupta, A.J., Samantaray, S.
Format: Article
Language:English
Subjects:
Asymptotic accuracy
Asymptotic preserving
Compressible euler system
Finite volume method
IMEX-RK Schemes
Incompressible euler system
The wave equation system
Zero mach number limit
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Summary:In this paper the analysis of an asymptotic preserving (AP) IMEX-RK finite volume scheme for the wave equation system in the zero Mach number limit is presented. An IMEX-RK methodology is employed to obtain a time semi-discrete scheme, and a space-time fully-discrete scheme is derived by using standard finite volume techniques. The existence of a unique numerical solution, its uniform stability with respect to the Mach number, and the accuracy at low Mach numbers are established for both time semi-discrete and space-time fully-discrete schemes. The AP property of the scheme is proved for a general class of IMEX schemes which need not be globally stiffly accurate. Extensive numerical case studies confirm uniform second order convergence of the scheme with respect to the Mach number and all the above-mentioned properties.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2021.126469