Speaker
Description
Mathematically, the double-porosity model leads to a system of coupled second-order parabolic equations with respect to the pressures in fractures and in the porous matrix. Such a system is characterized by the presence of diffusion terms describing the spatial redistribution of pressure and a reaction term responsible for inter porosity exchange.
In the present work, a probabilistic method for the numerical solution of a system of parabolic equations arising in filtration problems in fractured porous media is proposed. The calculation algorithm is based on the construction of a special Markov process and the use of unbiased Monte Carlo estimators for the approximate computation of the solution. The unbiasedness of the constructed estimator and the finiteness of its variance are established. A computational experiment confirming the convergence of the statistical estimators and the efficiency of the proposed algorithm is presented. A probabilistic representation of the solution to the initial-boundary value problem for a general system of parabolic equations was previously obtained by the authors in works [1,2]. In the present paper applies this approach to the filtration problem in a fractured porous medium.
References
- Raimova G.M. Probabilistic representation of the solution of the initial-boundary value problem for the system of parabolic equations // Theory of Probability and Its Applications. 2013. Vol. 57, No. 4. P. 688–697. DOI: 10.1137/S0040585X97986291.
- Rasulov A.S., Raimova G.M. A new algorithm for system of integral equations // Abstract and Applied Analysis. 2014. Vol. 2014. Article ID 236065.
DOI: 10.1155/2014/236065.
