Volume 56, Number 6, November-December 2022
|Page(s)||1911 - 1938|
|Published online||14 September 2022|
Penalization method for the Navier–Stokes–Fourier system
Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, CZ-11567 Praha 1, Czech Republic
2 Institute of Mathematics, Johannes Gutenberg-University Mainz, Staudingerweg 9, 55128 Mainz, Germany
3 Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics of the Comenius University Mlynská dolina, 84248 Bratislava, Slovakia
* Corresponding author: firstname.lastname@example.org
Accepted: 18 July 2022
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.
Mathematics Subject Classification: 35A01 / 76M12 / 76N06
Key words: Navier–Stokes–Fourier system / penalization method / Dirichlet problem / finite volume method
© The authors. Published by EDP Sciences, SMAI 2022
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