We apply the method of penalization to the Dirichlet problem for the Navier–Stokes–Fourier system governing the motion of a general viscous compressible fluid confined to a bounded Lipschitz domain. The physical domain is embedded into a large cube on which the periodic boundary conditions are imposed. The original boundary conditions are enforced through a singular friction term in the momentum equation and a heat source/sink term in the internal energy balance. The solutions of the penalized problem are shown to converge to the solution of the limit problem. In particular, we extend the available existence theory to domains with rough (Lipschitz) boundary. Numerical experiments are performed to illustrate the efficiency of the method.
Keywords: Navier–Stokes–Fourier system, penalization method, Dirichlet problem, finite volume method
@article{M2AN_2022__56_6_1911_0,
author = {Basari\'c, Danica and Feireisl, Eduard and Luk\'a\v{c}ov\'a-Medvid{\textquoteright}ov\'a, M\'aria and Mizerov\'a, Hana and Yuan, Yuhuan},
title = {Penalization method for the {Navier{\textendash}Stokes{\textendash}Fourier} system},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1911--1938},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {6},
doi = {10.1051/m2an/2022063},
mrnumber = {4481122},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2022063/}
}
TY - JOUR AU - Basarić, Danica AU - Feireisl, Eduard AU - Lukáčová-Medvid’ová, Mária AU - Mizerová, Hana AU - Yuan, Yuhuan TI - Penalization method for the Navier–Stokes–Fourier system JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2022 SP - 1911 EP - 1938 VL - 56 IS - 6 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2022063/ DO - 10.1051/m2an/2022063 LA - en ID - M2AN_2022__56_6_1911_0 ER -
%0 Journal Article %A Basarić, Danica %A Feireisl, Eduard %A Lukáčová-Medvid’ová, Mária %A Mizerová, Hana %A Yuan, Yuhuan %T Penalization method for the Navier–Stokes–Fourier system %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2022 %P 1911-1938 %V 56 %N 6 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2022063/ %R 10.1051/m2an/2022063 %G en %F M2AN_2022__56_6_1911_0
Basarić, Danica; Feireisl, Eduard; Lukáčová-Medvid’ová, Mária; Mizerová, Hana; Yuan, Yuhuan. Penalization method for the Navier–Stokes–Fourier system. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 6, pp. 1911-1938. doi: 10.1051/m2an/2022063
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