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Asymptotic preserving error estimates for numerical solutions of compressible Navier-Stokes equations in the low Mach number regime

SYSNO ASEP	0485868
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Asymptotic preserving error estimates for numerical solutions of compressible Navier-Stokes equations in the low Mach number regime
Author(s)	Feireisl, Eduard (MU-W)_{RID, SAI, ORCID} Lukáčová-Medviďová, M. (DE) Nečasová, Šárka (MU-W)_{RID, SAI, ORCID} Novotný, A. (FR) She, Bangwei (MU-W)_{SAI, RID, ORCID}
Source Title	Multiscale Modeling and Simulation. - : Society for Industrial and Applied Mathematics - ISSN 1540-3459 Roč. 16, č. 1 (2018), s. 150-183
Number of pages	34 s.
Language	eng - English
Country	US - United States
Keywords	Navier-Stokes system ; finite element numerical method ; finite volume numerical method ; asymptotic preserving schemes
Subject RIV	BA - General Mathematics
OECD category	Pure mathematics
R&D Projects	GA16-03230S GA ČR - Czech Science Foundation (CSF)
Institutional support	MU-W - RVO:67985840
UT WOS	000429645500006
EID SCOPUS	85045026178
DOI	10.1137/16M1094233
Annotation	We study the convergence of numerical solutions of the compressible Navier-Stokes system to its incompressible limit. The numerical solution is obtained by a combined finite element-finite volume method based on the linear Crouzeix-Raviart finite element for the velocity and piecewise constant approximation for the density. The convective terms are approximated using upwinding. The distance between a numerical solution of the compressible problem and the strong solution of the incompressible Navier-Stokes equations is measured by means of a relative energy functional. For barotropic pressure exponent $\gamma \geq 3/2$ and for well-prepared initial data we obtain uniform convergence of order $\cal O(\sqrt\Delta t, h^a, \varepsilon)$, $a = \min \ \frac{2 \gamma - 3 \gamma, 1\$. Extensive numerical simulations confirm that the numerical solution of the compressible problem converges to the solution of the incompressible Navier-Stokes equations as the discretization parameters $\Delta t$, $h$ and the Mach number $\varepsilon$ tend to zero.
Workplace	Mathematical Institute
Contact	Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757
Year of Publishing	2019

Number of the records: 1