Computational aspects in controlling filtration of fluids and gases in porous media

To control filtration of gases, liquid hydrocarbons, oil, and water in homogeneous and heterogeneous porous media, it is necessary to obtain a multivariate solution to systems of nonlinear or quasi-linear equations in partial differentials of the parabolic type that define hydrodynamic (mathematical) models of control objects. In this paper, we propose hierarchical multigrid variants of balance and variational methods together with methods of domain decomposition, splitting with respect to physical processes and spatial coordinates. The paper consists of two parts. In the first part we consider a model of single-phase filtration of gas in gas-field developing; in the second, a model of two-phase filtration of oil and water, i.e., oil fields. This statement proves the universal character of the proposed results. Due to the multilevel partition of the original initial boundary value problem, we can construct economical solution algorithms using multiprocessor computer systems of the cluster type of parallel action for equations of the model.