One approach to constructing a conservative difference scheme for the two-phase filtration problem

A numerical method for solving two-phase filtration problems is developed on the basis of the adaptive artificial viscosity method for the simulation of the continuity equation. The developed difference scheme has a second order of approximation in time and space. Numerical experiments were performed for the proposed two-phase filtration problems. Numerical calculations showed that the proposed method well traces the discontinuities of the numerical solution.