The homogenization of Stokes flows in random porous domains of general type

Article type: Research Article

Authors: Beliaev, Alexei^;

Affiliations: Water Problem Institute, Gubkina Streets, 3, 117971 Moscow, Russia E‐mail: [email protected]

Note: [] Temporary address: Faculty of Civil Engineering and Geosciences, Section of Hydrology and Ecology, Delft University of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands. E‐mail: [email protected].

Abstract: A new proof of the Darcy law is proposed in the framework of the homogenization theory. The starting point of the homogenization is an unsteady flow of compressible viscous liquid through a small‐scaled random porous domain. This non‐stationary microscopic flow is described by the Stokes equations supplemented by zero boundary conditions for the velocity field. The Darcy law is established for the leading term of the solution. The main geometric assumption on the structure is the connectedness of the porous domain. The set of assumptions contains neither a regularity of boundaries nor any quantitative properties appertaining to the connectedness.

Journal: Asymptotic Analysis, vol. 19, no. 2, pp. 81-94, 1999