(44) .)( FVbxWW
Now, substituting (44) into (15) and taking into
account
we obtain
(46) on ),(
(45) in ,0)(
0
2
xss
WsaCdif
6 Conclusion
In this paper, the issues of applying Monte-Carlo
algorithms to filtration problems are
investigated. We were able to apply the
algorithms of "random walk by spheres" and
"random walk by boundary" Monte-Carlo
methods to solve the stationary problem of
filtration of two immiscible inhomogeneous
incompressible liquids in a porous medium. We
have constructed a 𝜀 −biased estimate of the
solution and derivatives of the solution (the first
derivative of saturation, the first and second
derivatives of pressure) of the stationary problem
of two-phase filtration of incompressible
immiscible liquids in a porous medium. Using
the same Monte-Carlo algorithms, it is possible
to solve the filtration problem taking into
account temperature (i.e. the energy equation is
added to the filtration equations). The scientific
novelty of the research consists in the fact that,
theoretically and practically, the method of
statistical testing (Monte-Carlo) for solving
boundary value problems of stationary and non-
stationary filtration in areas of arbitrary
configuration, which has positive possibilities of
implementation on modern computers, is being
developed.
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WSEAS TRANSACTIONS on MATHEMATICS
DOI: 10.37394/23206.2022.21.88
M. Tastanov, A. Utemissova, F. Maiyer, R. Ysmagul