Volume 53, Number 6, November-December 2019
|Page(s)||1957 - 1979|
|Published online||15 November 2019|
Convergence of a finite volume scheme for the compressible Navier–Stokes system
Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic
2 Technische Universität Berlin, Straße des 17. Juni, Berlin, Germany
3 Institute of Mathematics, Johannes Gutenberg-University Mainz, Staudingerweg 9, 55 128 Mainz, Germany
4 Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics of the Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia
* Corresponding author: email@example.com
Accepted: 11 June 2019
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.
Mathematics Subject Classification: 35Q30 / 65N12 / 76M12 / 76NXX
Key words: Compressible Navier–Stokes system / convergence / dissipative measure valued solution / finite volume method
© EDP Sciences, SMAI 2019
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