Asymptotic-preserving IMEX schemes for the Euler equations of non-ideal gases

2024/02/14 by Orlando, Giuseppe, Bonaventura, Luca
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2402.09252

Abstract

We analyze schemes based on a general Implicit-Explicit (IMEX) time discretization for the compressible Euler equations of gas dynamics, showing that they are asymptotic-preserving (AP) in the low Mach number limit. The analysis is carried out for a general equation of state (EOS). We consider both a single asymptotic length scale and two length scales. We then show that, when coupling these time discretizations with a Discontinuous Galerkin (DG) space discretization with appropriate fluxes, a numerical method effective for a wide range of Mach numbers is obtained. A number of benchmarks for ideal gases and their non-trivial extension to non-ideal EOS validate the performed analysis.

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