Application of continuous symmetry groups for numerical solutions of two-phase filtration problems

Abstract

Abstract The method of numerical solution calculations for difference schemes on the basis of continuous symmetry groups has been presented for the two-phase flow equation. This method gives an opportunity to calculate numerical solutions using transformations of a symmetry group and known particular numerical solutions what allows to achieve an acceleration of serial numerical calculations by several orders. The families of invariant difference schemes have been obtained for one of generalized Buckley-Leverett equations - the Rapoport-Leas equation. A particular nonlinear equation of multiphase flow in fractured porous media with certain coefficients from the mentioned families is analyzed numerically by the presented method.