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Cybernetics And Systems Analysis
International Theoretical Science Journal
Volume 56 >>> № 3 MAY — JUNE 2020
UDC 517.9:519.6
V.M. Bulavatsky1, V.O. Bohaienko2


1 V.M. Glushkov Institute of Cybernetics, National Academy
of Sciences of Ukraine, Kyiv, Ukraine

 v_bulav@ukr.net

2 V.M. Glushkov Institute of Cybernetics, National Academy
of Sciences of Ukraine, Kyiv, Ukraine

 sevab@ukr.net

SOME BOUNDARY-VALUE PROBLEMS OF FRACTIONAL-DIFFERENTIAL
MOBILE-IMMOBILE MIGRATION DYNAMICS IN A PROFILE FILTRATION FLOW

Abstract. Within the framework of the fractional differential mathematical model, the formulation of boundary-value problems of convective diffusion of soluble substances with regard to immobilization under the conditions of stationary filtration of groundwater from the reservoir to drainage is performed. In the case of averaging the filtration rate over the complex potential region, closed solutions of boundary value problems corresponding to classical and nonlocal boundary conditions are obtained. In the general case of a variable filtration velocity, a technique is developed for the numerical solution of a boundary-value problem of convective diffusion in a fractional-differential formulation, the problems of parallelizing computations are covered, and the results of computer experiments are presented.

Keywords: mathematical modeling, nonclassical models, convective-diffusion process, mobile-immobile porous media migration models, fractional diffusion equation, boundary-value problems, approximation solutions.



FULL TEXT

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