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Journal Articles Numerical Methods for Partial Differential Equations Year : 2020

An asymptotic preserving scheme on staggered grids for the barotropic Euler system in low Mach regimes

Abstract

We present a new scheme for the simulation of the barotropic Euler equation in low Mach regimes. The method uses two main ingredients. First, the system is treated with a suitable time splitting strategy, directly inspired from [J. Haack, S. Jin, J.-G. Liu, Comm. Comput. Phys., 12 (2012) 955-980], that separates low and fast waves. Second, we adapt a numerical scheme where the discrete densities and velocities are stored on staggered grids, in the spirit of MAC methods, and with numerical fluxes derived form the kinetic approach. We bring out the main properties of the scheme in terms of consistency, stability, and asymptotic behaviour, and we present a series of numerical experiments to validate the method.
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Dates and versions

hal-02418641 , version 1 (10-12-2020)

Identifiers

  • HAL Id : hal-02418641 , version 1

Cite

Thierry Goudon, Julie Llobell, Sebastian Minjeaud. An asymptotic preserving scheme on staggered grids for the barotropic Euler system in low Mach regimes. Numerical Methods for Partial Differential Equations, 2020, 36 (5), pp.1098-1128. ⟨hal-02418641⟩
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