Convergence of a finite volume scheme for the compressible Navier-Stokes system

0511292 - MÚ 2020 RIV FR eng J - Journal Article
Feireisl, Eduard - Lukáčová-Medviďová, M. - Mizerová, Hana - She, Bangwei
Convergence of a finite volume scheme for the compressible Navier-Stokes system.
E S A I M: Mathematical Modelling and Numerical Analysis. Roč. 53, č. 6 (2019), s. 1957-1979. ISSN 0764-583X. E-ISSN 1290-3841
R&D Projects: GA ČR GA16-03230S; GA ČR(CZ) GA18-05974S
Institutional support: RVO:67985840
Keywords : compressible Navier–Stokes system * convergence * dissipative measure valued solution * finite volume method
OECD category: Pure mathematics
Impact factor: 1.353, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1051/m2an/2019043

We study convergence of a finite volume scheme for the compressible (barotropic) Navier–Stokes system. First we prove the energy stability and consistency of the scheme and show that the numerical solutions generate a dissipative measure-valued solution of the system. Then by the dissipative measure-valued-strong uniqueness principle, we conclude the convergence of the numerical solution to the strong solution as long as the latter exists. Numerical experiments for standard benchmark tests support our theoretical results.
Permanent Link: http://hdl.handle.net/11104/0301596