Numerical solution of one dimensional filtration of three phase compressible fluid through porous medium in a class of discontinuous functions

A numerical method is proposed for a system of nonlinear partial differential equations which describe the flow of three phased mixture in a porous medium taking the capillary pressure into account. For this aim, firstly, by splitting the system of differential equations with respect to physical factors, a special auxiliary problem is introduced. Then, on the basis of this auxiliary problem, the finite differences method for solving the solution of the main problem in a class of discontinuous functions is developed, which accurately describes the whole properties of the physical problem at interest. Some results of the numerical experiments of physical interest are presented.