WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 21, 2022
The Stationary Problem of Two-Phase Filtration by the Monte-Carlo Method: Solutions and Applications
Authors: , , ,
Abstract: This article is devoted to solving the problems of applying Monte-Carlo algorithms to filtration problems. The "random walk by spheres" and "random walk by boundary" algorithms of Monte-Carlo methods are used to solve the stationary problem of filtration of two immiscible inhomogeneous incompressible liquids in a porous medium. Estimates constructed using the "random walk by spheres" and "random walk by boundary" algorithms of Monte-Carlo methods will be mostly ε−biased. Unbiased estimates are in most cases unrealizable on a computer, since with a probability of 1 they do not go to the boundary of the region, and therefore are of little use. In practice, they are usually limited to only the first two points of evaluation.
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Keywords: Monte-Carlo method, continuity equation, Dirichlet problem, Markov chains, algorithms of random walk by spheres, random walk by boundary, estimation of the solution and derivatives of the solution
Pages: 770-778
DOI: 10.37394/23206.2022.21.88