Geodesic
Application of Monte Carlo methods for solving the regular and degenerate problem of two-phase filtration
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 80 (2022), pp. 147-156 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: Monte Carlo method, continuity equation, Dirichlet problem, estimate of the solution and its derivatives.
Mots-clés : Markov chains 
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     author = {M. G. Tastanov and A. A. Utemissova and F. F. Maiyer},
     title = {Application of {Monte} {Carlo} methods for solving the regular and degenerate problem of two-phase filtration},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {147--156},
     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/VTGU_2022_80_a12/}
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M. G. Tastanov; A. A. Utemissova; F. F. Maiyer. Application of Monte Carlo methods for solving the regular and degenerate problem of two-phase filtration. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 80 (2022), pp. 147-156. http://geodesic.mathdoc.fr/item/VTGU_2022_80_a12/

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