Statistic modeling and Monte Carlo methods
A small perturbation method is developed for the construction of a stochastic model of transport in a porous medium. Under the assumption of small fluctuations of the hydraulic conductivity we construct explicitly the spectral tensor of the velocity field. In the case of gaussian distribution of the velocity field we use the constructed spectra for simulating the Lagrangian trajectory according to the technique given in . This results in a Eulerian-Lagrangian stochastic model of particle's transport in this kind of velocity field and in calculating the main Lagrangian statistical characteristics. This approach is a genegalization of the work of authors , where we have considered the whole space. Essentially new is the result about the existence of a superdiffusion regime.
References. 1. Sabelfeld K.K. Monte Carlo Methods in Boundary Value Problems. Springer, New-York - Tokyo - Berlin, 1991. 2. K. Sabelfeld and D. Kolyukhin. Eulerian model for the flow simulation in porous media. Monte Carlo Methods and Applications. Vol.9, N3, 271-290.
Note. Abstracts are published in author's edition
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