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A finite volume scheme for the Euler system inspired by the two velocities approach
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SYSNO ASEP 0521527 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A finite volume scheme for the Euler system inspired by the two velocities approach Author(s) Feireisl, Eduard (MU-W) RID, SAI, ORCID
Lukáčová-Medviďová, M. (DE)
Mizerová, Hana (MU-W) SAI, RIDSource Title Numerische Mathematik - ISSN 0029-599X
Roč. 144, č. 1 (2020), s. 89-132Number of pages 44 s. Language eng - English Country DE - Germany Keywords Boltzmann equation ; Euler system ; moment equations Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA18-05974S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000492572700001 EID SCOPUS 85074617198 DOI 10.1007/s00211-019-01078-y Annotation We propose a new finite volume scheme for the Euler system of gas dynamics motivated by the model proposed by H. Brenner. Numerical viscosity imposed through upwinding acts on the velocity field rather than on the convected quantities. The resulting numerical method enjoys the crucial properties of the Euler system, in particular positivity of the approximate density and pressure and the minimal entropy principle. In addition, the approximate solutions generate a dissipative measure-valued solutions of the limit system. In particular, the numerical solutions converge to the smooth solution of the system as long as the latter exists. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2021 Electronic address https://doi.org/10.1007/s00211-019-01078-y
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