Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Arutyunyan R. V. Stochastic Simulation of Diffusion Filtering. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 1, pp. 5-12. DOI: 10.18500/1816-9791-2016-16-1-5-12, EDN: VUSOCT

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
14.03.2016
Full text:
(downloads: 178)
Language: 
Russian
Heading: 
UDC: 
510: 53.072: 621.1.016.4(03)
EDN: 
VUSOCT

Stochastic Simulation of Diffusion Filtering

Autors: 
Arutyunyan Robert Vladimirovich, Moscow Technical University of Communications and Informatics, Russia
Abstract: 

Formulated and investigated is the system of kinetic equations describing the process of diffusion filtering based on a stochastic approach. The theorem of existence and uniqueness of the solution for the case of a continuous density is prove. We obtain the representation of solution in the form of a uniformly convergent and asymptotic series,and explore the nature of its behavior at infinity. The concrete particular cases such as the density of the delta function and a uniform distribution are considered.Thefinite-difference scheme for the solution of the corresponding Cauchy problem on finite intervals of time is constructed and justified. The results of computer simulation are given.

References: 
  1. Reznikov G. D., Zhikhar’ A. S. Chislenno-analiticheskii podkhod k modelirovaniiu perenosa chastits v fil’truiushchem sloe [Numerical and analytical approach to the modeling of the transport of particles in the filter bed]. Matematicheskoe modelirovanie [Mathematical modeling], 1995, vol. 7, no. 6, pp. 118–125 (in Russian).
  2. Gavich I. K., Zektser I. S., Kovalevskii V. S., Iazvin L. S., Pinneker E. V., Bondarenko S. S., Borevskii L. V., Dziuba A. A. Osnovy gidrogeologii. Gidrogeodinamika [Fundamentals of hydrogeology. Hidrogeodinamika]. Novosibirsk, Nauka, 1983, 241 p. (in Russian).
  3. Gurevich A. E. Prakticheskoe rukovodstvo po izucheniiu dvizheniia podzemnykh vod pri poiskakh poleznykh iskopaemykh [A Practical Guide to the study of groundwater movement in the search for minerals]. Leningrad, Nedra, 1980, 216 p. (in Russian).
  4. Kolesnikov A. V. Matematicheskoe modelirovanie fil’tratsii zhidkosti v neodnorodnykh i periodicheskikh poristykh telakh metodom odnorodnoanizotropnogo ekvivalentirovaniia [Mathematical modeling of fluid flow in heterogeneous and periodic porous bodies by homogeneous anisotropic equivalenting] : avtoref. dis. ... kand. tekhn. nauk / Severo-Kavkazskii federal’nyi universitet. Stavropol’, 2014 (in Russian).
  5. Spravochnik po spetsial’nym funktsiiam [Handbook of special functions] / eds. M. Abramovitsa, I. Stigan. Moscow, Nauka, 1979, 832 p. (in Russian).
  6. Trenogin V. A. Funktsional’nyi analiz [Function analysis]. Moscow, Nauka, 1980, 496 p. (in Russian).
Received: 
10.10.2015
Accepted: 
28.02.2016
Published: 
31.03.2016