In the paper, we propose a modern mathematical method for solving seepage problems in multiscale porous media. We present a discrete variational formulation for a Discontinuous Galerkin Method (DG-method) with special stabilizing parameters. The DG-method is used for solving the single-phase fluid flow problem with full permeability tensor of the second rank in the macrolevel medium. A problem of homogenizing the heterogeneous mesolevel medium with non-periodic inclusions is considered. An algorithm for solving an inverse data problem is based on the Fletcher-Reeves method and the local Newton method. Mathematical modeling results of solving the seepage problem in the anisotropic heterogeneous and efficient media are given. A comparative analysis of the obtained mathematical modeling results is carried out. Keywords: seepage problem, Discontinuous Galerkin Method, permeability tensor, homogenization.
