Comparative analysis of explicit type algorithms for solving problems of filtration with the use of hyperbolized equations

The work is devoted to the development of explicit-type computational algorithms for modeling multiphase flow of slightly compressible fluid in the subsurface. Two approaches to the derivation of a hyperbolized system of filtration equations are considered. One of the models is developed on the basis of the principle of minimal sizes and the technique of differential approximations. The other model is obtained by introducing the mass flux relaxation into the continuity equation. Algorithms are proposed that use the approximation of modified equations by three-level explicit difference schemes. These two approaches are compared on test predictions. The algorithms are comparable in computational costs and can increase the time step by at least an order of magnitude compared to the implementation of the classical model by two-level explicit schemes.