Nontraditional mathematical models of fluid filtration in porous media

Consideration was given to the multilevel variants of parallelization of computations in mathematical modeling of the hydrodynamical processes of fluid filtration in porous media. The proposed approach to the design of numerical models is based on the most important advances of numerical mathematics such as different versions of the methods of finite elements, finite volumes, finite super-elements, multiple grids, and domain decomposition for elliptic, parabolic, and hyperbolic quasilinear equations of mathematical physics. The structure of hierarchical decomposition of the model for organization of parallel computations was chosen with regard for the characteristics of the subject of modeling, that is, for layered and spatial nonuniformity of the porous medium and filtration characteristics of the fluids.