On a Solutonto the Statonary Problem of Two-Phase Filtration by the Monte Carlo Method
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 "sphere walk" and "boundary walk" algorithms of Monte Carlo methods are used to solve the stationary problem of filtering two immiscible inhomogeneous incompressible liquids in a porous medium. Estimates constructed using the "sphere walk" and "boundary walk" 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.