Bulavatsky V.M., Bohaienko V.O.
Some boundary-value problems of fractional-differential mobile-immobile migration dynamics in a profile filtration flow

Within the framework of 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 profile filtration of groundwater from reservoir to drainage is performed. In 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 the variable filtration velocity, a technique is developed for the numerical solution to the boundary-value problem of convective diffusion in a fractional-differential formulation, the problems of parallelizing computations are covered, and the results of the computer experiments are presented. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: approximation solutions, boundary-value problems, convective-diffusion process, fractional-diffusion equations, mathematical modeling, mobile–immobile porous media migration, nonclassical models, Filtration, Groundwater, Complex potentials, Computer experiment, Convective diffusion, Filtration velocity, Fractional differential, Migration dynamics, Non-local boundary conditions, Numerical solution, Boundary value problems

Cite:
Bulavatsky V.M., Bohaienko V.O. (2020). Some boundary-value problems of fractional-differential mobile-immobile migration dynamics in a profile filtration flow. Cybernetics and Systems Analysis, 56 (3), 80–96. doi: https://doi.org/10.1007/s10559-020-00257-2 http://jnas.nbuv.gov.ua/article/UJRN-0001121521 [In Russian].