Smoothed particle hydrodynamics method for numerical solution of multidimensional filtering problems

The paper is devoted to solving the filtering problem for a mixture of water, gas, and oil in a homogeneous porous medium. The basic equations of filtration theory are converted into a special form for the numerical approximation with the smoothed particle hydrodynamics (SPH) method. A numerical difference scheme is constructed on the basis of SPH method. An algorithm for setting the boundary conditions is proposed and a number of isothermal 1D and 2D tests on the filtering process simulation for a mixture of water, oil, and gas.