Асимптотические и численные методы моделирования диффузной фильтрации

In this article for the study of the process of overgrowing holes in the lattice structure, which plays the role of a filter, used a stochastic approach. Formulated and studied the system of kinetic equations that model the process of diffusion filtering based on this approach. In contrast to the well-known works, where the absorption parameter was calculated on a computer using statistical tests, the basic characteristics of the filter structure in the current study were determined by deterministic methods. The theorem of existence and uniqueness of solutions for the case of continuous density is proved. Representation of solution in the form of a uniformly convergent series and asymptotic, and studied its behavior at infinity. The concrete particular cases such as the density of the delta function and a uniform distribution are studied. Constructed and proved finite-difference scheme for the solution of the corresponding Cauchy problem on a finite time interval. Simulation results on a computer are considered. It is shown that the finite-difference scheme of the first order is almost acceptable when a computer calculation. Investigated in the model, despite a number of simplifying assumptions, it gives an overview of the filtering process in lattice structures. The results can be developed, especially in respect of the functional classes density distribution of the size of a particle filter and a method of asymptotic estimates in the interval.