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Homogenization of MHD flows in porous media Научная публикация

Журнал Journal of Differential Equations
ISSN: 0022-0396
Вых. Данные Год: 2022, Том: 339, Страницы: 90-133 Страниц : 44 DOI: 10.1016/j.jde.2022.08.014
Ключевые слова Averaging of a nonlinear differential system; Homogenization; Magnetohydrodynamic (MHD) flow in porous media; Maxwell equations; Stokes equations; Two-scale equations
Авторы Youcef Amirat 1 , Hamdache Kamel 2 , Shelukhin V.V. 3
Организации
1 Université Clermont Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand, France
2 Léonard de Vinci Pôle Universitaire, Research Center, 92 916 Paris La Défense Cedex, France
3 Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences,

Информация о финансировании (1)

1 Министерство науки и высшего образования Российской Федерации FWGG-2021-0002

Реферат: The paper is concerned with the homogenization of a nonlinear differential system describing the flow of an electrically conducting, incompressible and viscous Newtonian fluid through a periodic porous medium, in the presence of a magnetic field. We introduce a variational formulation of the differential system equipped with boundary conditions. We show the existence of a solution of the variational problem, and derive uniform estimates of the solutions depending on the characteristic parameters of the flow. Using the two-scale convergence method, we rigorously derive a two-scale equation for the two-scale current density, and a two-pressure Stokes system. We derive, in the case of constant magnetic permeability, an explicit relation expressing the macroscopic velocity as a function of the macroscopic Lorentz force, the pressure gradient, the external body force, and the macroscopic current density, via two permeability filtration tensors. When the magnetic field is absent, this relation reduces to the Darcy law.
Библиографическая ссылка: Youcef A. , Hamdache K. , Shelukhin V.V.
Homogenization of MHD flows in porous media
Journal of Differential Equations. 2022. V.339. P.90-133. DOI: 10.1016/j.jde.2022.08.014 WOS Scopus РИНЦ OpenAlex
Даты:
Поступила в редакцию: 15 дек. 2021 г.
Принята к публикации: 17 авг. 2022 г.
Идентификаторы БД:
Web of science: WOS:000863272900002
Scopus: 2-s2.0-85137087624
РИНЦ: 56686654
OpenAlex: W4293799866
Цитирование в БД:
БД Цитирований
Scopus 2
OpenAlex 3
РИНЦ 2
Web of science 3
Альметрики: