The Stationary Problem of Two-Phase Filtration by the Monte-Carlo Method: Solutions and Applications
Meyrambek G. Tastanov, Anar A. Utemissova, Fedor F. Maiyer, R.S. Ysmagul · WSEAS TRANSACTIONS ON MATHEMATICS · 2022
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.