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Article

Kučera, Václav ; Lukáčová-Medviďová, Mária ; Noelle, Sebastian ; Schütz, Jochen
Low-Mach consistency of a class of linearly implicit schemes for the compressible Euler equations. (English). In: Chleboun, J., Kůs, P., Přikryl, P., Rozložník, M., Segeth, K. and Šístek, J. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Hejnice, June 21-26, 2020. Institute of Mathematics CAS, Prague, 2021. pp. 69-78
MSC: 65M12, 76B03, 76M45, 76N10 | DOI: 10.21136/panm.2020.07
Keywords:
asymptotic preserving schemes; compressible Euler equations; low-Mach limit; Hilbert expansion
Summary:
In this note, we give an overview of the authors' paper [6] which deals with asymptotic consistency of a class of linearly implicit schemes for the compressible Euler equations. This class is based on a linearization of the nonlinear fluxes at a reference state and includes the scheme of Feistauer and Ku\v{c}era [3] as well as the class of RS-IMEX schemes [8,5,1] as special cases. We prove that the linearization gives an asymptotically consistent solution in the low-Mach limit under the assumption of a discrete Hilbert expansion. The existence of the Hilbert expansion is shown under simplifying assumptions.
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