The Study of Filtration of Two Phase Fluid in a Porous Medium in a Class of Discontinuous Functions

In this study a new numerical method for obtaining the solution of the problem for 2-D system of equations which describes the filtration of the multi-phase fluid in porous medium with suitable initial and boundary conditions is proposed. For this aim, the special auxiliary problem having some advantages over the main problem is introduced. An efficient and accurate numerical algorithm based on the auxiliary problem is derived. Furthermore, some results of numerical experiments from the related subjects of physics are presented.