The Stationary Problem of Two-Phase Filtration by the Monte-Carlo Method: Solutions and Applications
TASTANOV M. UTEMISSOVA A. MAIYER F. YSMAGUL R.
2022World Scientific and Engineering Academy and Society
WSEAS Transactions on Mathematics
2022#21770 - 778 pp.
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.
algorithms of random walk by spheres , continuity equation , Dirichlet problem , estimation of the solution and derivatives of the solution , Markov chains , Monte-Carlo method , random walk by boundary
Text of the article Перейти на текст статьи
Kostanay Regional University, Baytursynov Street 47, Kostanay, 110000, Kazakhstan
Kostanay Regional University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026