Abstract: 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.

Cite: 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

Dates:

Submitted:	Dec 15, 2021
Accepted:	Aug 17, 2022

Identifiers:

Web of science:	WOS:000863272900002
Scopus:	2-s2.0-85137087624
Elibrary:	56686654
OpenAlex:	W4293799866

Citing:

DB	Citing
Scopus	2
OpenAlex	3
Elibrary	2
Web of science	3

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