A finite volume scheme for the Euler system inspired by the two velocities approach

0521527 - MÚ 2021 RIV DE eng J - Journal Article
Feireisl, Eduard - Lukáčová-Medviďová, M. - Mizerová, Hana
A finite volume scheme for the Euler system inspired by the two velocities approach.
Numerische Mathematik. Roč. 144, č. 1 (2020), s. 89-132. ISSN 0029-599X. E-ISSN 0945-3245
R&D Projects: GA ČR(CZ) GA18-05974S
Institutional support: RVO:67985840
Keywords : Boltzmann equation * Euler system * moment equations
OECD category: Pure mathematics
Impact factor: 2.223, year: 2020
Method of publishing: Limited access
https://doi.org/10.1007/s00211-019-01078-y

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.
Permanent Link: http://hdl.handle.net/11104/0306126