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Journal of Scientific Computing

Erschienen in:

28.08.2019

The Active Flux Scheme on Cartesian Grids and Its Low Mach Number Limit

verfasst von: Wasilij Barsukow, Jonathan Hohm, Christian Klingenberg, Philip L. Roe

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2019

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Abstract

Finite volume schemes for hyperbolic conservation laws require a numerical intercell flux. In one spatial dimension the numerical flux can be successfully obtained by solving (exactly or approximately) Riemann problems that are introduced at cell interfaces. This is more challenging in multiple spatial dimensions. The active flux scheme is a finite volume scheme that considers continuous reconstructions instead. The intercell flux is obtained using additional degrees of freedom distributed along the cell boundary. For their time evolution an exact evolution operator is employed, which naturally ensures the correct direction of information propagation and provides stability. This paper presents an implementation of active flux for the acoustic equations on two-dimensional Cartesian grids and demonstrates its ability to simulate discontinuous solutions with an explicit time stepping in a stable manner. Additionally, it is shown that the active flux scheme for linear acoustics is low Mach number compliant without the need for any fix.

Vorheriger Artikel Numerical Approximations for the Tempered Fractional Laplacian: Error Analysis and Applications

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Titel: The Active Flux Scheme on Cartesian Grids and Its Low Mach Number Limit
verfasst von: Wasilij Barsukow
Jonathan Hohm
Christian Klingenberg
Philip L. Roe
Publikationsdatum: 28.08.2019
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2019
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-019-01031-z

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