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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00485868" target="_blank" >RIV/67985840:_____/18:00485868 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1137/16M1094233" target="_blank" >http://dx.doi.org/10.1137/16M1094233</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/16M1094233" target="_blank" >10.1137/16M1094233</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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 $cal O(sqrtDelta t, h^a, varepsilon)$, $a = min frac{2 gamma - 3 gamma, 1$. 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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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 $cal O(sqrtDelta t, h^a, varepsilon)$, $a = min frac{2 gamma - 3 gamma, 1$. 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA16-03230S" target="_blank" >GA16-03230S: Termodynamicky konzistentni modely pro proudění tekutin: matematická teorie a numerické řešení</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Multiscale Modeling and Simulation

ISSN

1540-3459

e-ISSN

—

Svazek periodika

16

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

34

Strana od-do

150-183

Kód UT WoS článku

000429645500006

EID výsledku v databázi Scopus

2-s2.0-85045026178