Asymptotic preserving error estimates for numerical solutions of compressible Navier-Stokes equations in the low Mach number regime
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Asymptotic preserving error estimates for numerical solutions of compressible Navier-Stokes equations in the low Mach number regime
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA16-03230S" target="_blank" >GA16-03230S: Thermodynamically consistent models for fluid flows: mathematical theory and numerical solution</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Multiscale Modeling and Simulation
ISSN
1540-3459
e-ISSN
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Volume of the periodical
16
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
34
Pages from-to
150-183
UT code for WoS article
000429645500006
EID of the result in the Scopus database
2-s2.0-85045026178