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An asymptotic preserving scheme on staggered grids for the barotropic Euler system in low Mach regimes
Author(s) -
Goudon Thierry,
Llobell Julie,
Minjeaud Sebastian
Publication year - 2020
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22466
Subject(s) - barotropic fluid , mach number , mathematics , euler equations , euler system , scheme (mathematics) , euler's formula , stability (learning theory) , series (stratigraphy) , consistency (knowledge bases) , mathematical analysis , computer science , mechanics , physics , geometry , paleontology , machine learning , biology
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 the previous study 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 from the kinetic approach. We bring out the main properties of the scheme in terms of consistency, stability, and asymptotic behavior, and we present a series of numerical experiments to validate the method.