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Asymptotic preserving error estimates for numerical solutions of compressible Navier-Stokes equations in the low Mach number regime
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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, ORCIDSource Title Multiscale Modeling and Simulation. - : Society for Industrial and Applied Mathematics - ISSN 1540-3459
Roč. 16, č. 1 (2018), s. 150-183Number 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
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