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

0485868 - MÚ 2019 RIV US eng J - Journal Article
Feireisl, Eduard - Lukáčová-Medviďová, M. - Nečasová, Šárka - Novotný, A. - She, Bangwei
Asymptotic preserving error estimates for numerical solutions of compressible Navier-Stokes equations in the low Mach number regime.
Multiscale Modeling and Simulation. Roč. 16, č. 1 (2018), s. 150-183. ISSN 1540-3459. E-ISSN 1540-3467
R&D Projects: GA ČR GA16-03230S
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : Navier-Stokes system * finite element numerical method * finite volume numerical method * asymptotic preserving schemes
OECD category: Pure mathematics
Impact factor: 1.940, year: 2018
http://epubs.siam.org/doi/10.1137/16M1094233

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.
Permanent Link: http://hdl.handle.net/11104/0280797