Low-Mach consistency of a class of linearly implicit schemes for the compressible Euler equations
| Autor: | Jochen Schütz, Sebastian Noelle, Václav Kučera, Maria Lukáčová-Medviďová |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Class (set theory)
Hilbert expansion State (functional analysis) low-Mach limit Euler equations compressible Euler equations symbols.namesake Nonlinear system Linearization Consistency (statistics) Scheme (mathematics) symbols Applied mathematics Limit (mathematics) asymptotic preserving schemes Mathematics |
| Popis: | 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. The work of V. Kučera is supported by the Czech Science Foundation, project No. 20-01074S. The work of M. Lukáčová has been supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - TRR/SFB 146 - Project number 233630050, TRR/SFB 165 Waves to Weather - Project A2, and by the Mainz Institute of Multiscale Modelling. The work of S. Noelle was funded funded by the DFG Projektnummer 320021702/GRK2326. |
| Databáze: | OpenAIRE |
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