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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

IMA Journal of Numerical Analysis

ISSN

0272-4979

e-ISSN

—

Svazek periodika

39

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

24

Strana od-do

2045-2068

Kód UT WoS článku

000491253300015

EID výsledku v databázi Scopus

2-s2.0-85074151949