engleski

Application of very weak formulation on homogenization of boundary value problems in porous media

The goal of this paper is to present a different approach to homogenization of the Dirichlet boundary value problem in porous medium. Unlike standard the energy method or the method of the two-scale convergence, this approach is not based on the weak formulation of the problem but on the very weak formulation. To illustrate the method and its advantages we treat the stationary, incompressible Navier-Stokes system with non-homogeneous Dirichlet boundary condition in periodic porous medium. The non- zero velocity trace on the boundary of solid inclusion yields a non- standard addition to the source term in the Darcy law. In addition, the homogenized model is not incompressible.

Homogenization ; porous medium ; Navier-Stokes system ; very weak formulation

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