Convergent numerical method for the Navier-Stokes-Fourier system: a stabilized scheme

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00509632" target="_blank" >RIV/67985840:_____/19:00509632 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1093/imanum/dry057" target="_blank" >http://dx.doi.org/10.1093/imanum/dry057</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1093/imanum/dry057" target="_blank" >10.1093/imanum/dry057</a>

Result language

angličtina

Original language name

Convergent numerical method for the Navier-Stokes-Fourier system: a stabilized scheme

Original language description

We propose a combined finite volume--finite element method for the compressible Navier–Stokes–Fourier system. A finite volume approximation is used for the density and energy equations while a finite element discretization based on the nonconforming Crouzeix–Raviart element is applied to the momentum equation. We show the stability, the consistency and finally the convergence of the scheme (up to a subsequence) toward a suitable weak solution. We are interested in the diffusive term in the form of divergence of the symmetric velocity gradient instead of the classical Laplace form appearing in the momentum equation. As a consequence, there emerges the need to add a stabilization term that substitutes the role of Korn’s inequality which does not hold in the Crouzeix–Raviart element space. The present work is a continuation of Feireisl, E., Hošek, R. & Michálek, M. (2016, A convergent numerical method for the Navier–Stokes–Fourier system. IMA J. Numer. Anal., 36, 1477--1535), where a similar scheme is studied for the case of classical Laplace diffusion. We compare the two schemes and point out that the discretization of the energy diffusion terms in the reference scheme is not compatible with the model. Finally, we provide several numerical experiments for both schemes to demonstrate the numerical convergence, positivity of the discrete density, as well as the difference between the schemes.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

IMA Journal of Numerical Analysis

ISSN

0272-4979

e-ISSN

—

Volume of the periodical

39

Issue of the periodical within the volume

4

Country of publishing house

GB - UNITED KINGDOM

Number of pages

24

Pages from-to

2045-2068

UT code for WoS article

000491253300015

EID of the result in the Scopus database

2-s2.0-85074151949