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Title: | Low-Mach consistency of a class of linearly implicit schemes for the compressible Euler equations | Authors: | Kučera, Václav Lukáčová-Medviďová, Mária Noelle, Sebastian SCHUETZ, Jochen |
Editors: | Chleboun, J. Kus, P. Prikryl, P. Rozložník, M. Segeth, K. Sistek, J. |
Issue Date: | 2021 | Publisher: | ACAD SCIENCES CZECH REPUBLIC | Source: | J. Chleboun, P. Kůs, P. Přikryl, M. Rozložník, K. Segeth, J. Šístek (Ed.). Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar, Institute of Mathematics CAS, ACAD SCIENCES CZECH REPUBLIC, p. 69 -78 | Abstract: | 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. | Keywords: | asymptotic preserving schemes;compressible Euler equations;low-Mach limit;Hilbert expansion | Document URI: | http://hdl.handle.net/1942/34275 | ISBN: | 9788085823714 | DOI: | 10.21136/panm.2020.07 | ISI #: | WOS:000672803500007 | Category: | C1 | Type: | Proceedings Paper | Validations: | ecoom 2022 |
Appears in Collections: | Research publications |
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PANM_20-2020-1_10.pdf | Published version | 359.49 kB | Adobe PDF | View/Open |
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