Efficient Numerical Method of the 1D Motion of Two-Phase Fluid through Porous Medium in a Class of Discontinuous Functions

In this paper a new numerical method for nonlinear system of partial differential equations which describes motion of a two-phase compressible fluid in microscopic porous medium in a class of discontinuous functions is suggested. For this aim, at first, the system of equations is split in two equations according to physical parameters. First one with respect to water saturation, and the other one with respect to pressure. Then, the special auxiliary problem having some advantages over the main problem is introduced. This auxiliary problem permits to develop the efficient numerical algorithm for obtaining the solution. Using the solution of the auxiliary problem, the solution of the main problem, which expresses all the physical properties is found.