Mathematical modeling of one-phase filtration in randomly inhomogeneous porous media

This work investigates the problem of homogenization for media, the parameters of which are stochastic functions with known properties. On the basis of direct mathematical modeling of a problem (one-dimensional parabolic equation) the efficiency of different methods of average is investigated using both statistical estimation and the determined upscaling procedures. The problem on existence and definition of an effective coefficient of conductivity is researched, offering the criterion such as a median one for definition of the permissible solution of an average problem. In outcome is obtained, that when correlation radius is comparable with dimension of a spatial difference grid cells, it is necessary to esteem models with non-local relation of a flow to a gradient.