Application of Monte Carlo methods for solving the regular and degenerate problem of two-phase filtration

One of popular mathematical models of filtration is the classical elastic regime model describing the nonstationary equilibrium filtration. It is also called the Muskat-Leverett model. Solving filtration problems by Monte Carlo methods makes it possible to find the solution of the problem at an individual point of the domain and to estimate derivatives of the solution. This paper is devoted to applying algorithms of the Monte Carlo method to problems of filtration. The Monte Carlo algorithms of random walk by spheres and on boundaries are used for solving the stationary problem of filtration of two immiscible inhomogeneous incompressible fluids in a porous medium and for estimating the solution and the derivatives of the solution of this problem.