An asymptotic preserving scheme on staggered grids for the barotropic Euler system in low Mach regimes. Issue 5 (23rd January 2020)

• Record Type: Journal Article
• Authors: Goudon, Thierry; Llobell, Julie; Minjeaud, Sebastian
• Is Part Of: Numerical methods for partial differential equations. Volume 36:Issue 5(2020)
• Page Start: 1098
• Page End: 1128
• Publication Date: 2020-01-23
• Subjects: asymptotic preserving schemes -- low Mach regimes -- staggered grids; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22466
• Languages: English
• ISSNs: 0749-159X

Abstract

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 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.