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

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...

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Bibliographic Details
Published in:ESAIM. Mathematical modelling and numerical analysis 2019-11, Vol.53 (6), p.1957-1979
Main Authors: Feireisl, Eduard, Lukáčová-Medvid’ová, Mária, Mizerová, Hana, She, Bangwei
Format: Article
Language:English
Subjects:
35Q30
65N12
76M12
76NXX
Compressibility
Compressible Navier–Stokes system
Computational fluid dynamics
Convergence
dissipative measure valued solution
Finite volume method
Fluid flow
Navier-Stokes equations
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Summary: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.
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2019043