WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 23, 2024
On Solving the Regular Problem of Two-Phase Filtration Taking Into Account The Energy and one Model Problem of Filtration in Potentials by Monte Carlo Methods
Authors: , , , ,
Abstract: It should be noted that in some practical tasks, it is impossible not to take into account the temperature change. In this case, the energy equation should be added to the filtration equations. The algorithms of «random walk by spheres» and «random walk along boundaries» of Monte Carlo methods are used to solve regular degenerate filtration problems of two immiscible inhomogeneous incompressible liquids in a porous medium. The derivatives of the solution are evaluated using Monte Carlo methods. A model problem of filtration of a two-phase incompressible liquid with capillary forces is considered.
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Keywords: Monte Carlo method, Dirichlet problem, Markov chains, Levy function, unbiased estimation of the solution, integral operator
Pages: 154-159
DOI: 10.37394/23206.2024.23.18