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Penalization method for the Navier-Stokes-Fourier system

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    0561461 - MÚ 2023 RIV FR eng J - Journal Article
    Basarić, Danica - Feireisl, Eduard - Lukáčová-Medviďová, M. - Mizerová, Hana - Yuan, Y.
    Penalization method for the Navier-Stokes-Fourier system.
    ESAIM. Mathematical Modelling and Numerical Analysis. Roč. 56, č. 6 (2022), s. 1911-1938. ISSN 2822-7840. E-ISSN 2804-7214
    R&D Projects: GA ČR(CZ) GA21-02411S
    Institutional support: RVO:67985840
    Keywords : Navier-Stokes-Fourier system * penalization method * Dirichlet problem * finite volume method
    OECD category: Pure mathematics
    Method of publishing: Open access

    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.
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