Bulavatsky V.M., Bohaienko V.O.
Numerical simulation of fractional-differential filtration-consolidation dynamics within the framework of models with non-singular kernel

Non-classical mathematical models to describe the fractional-differential filtration-consolidation dynamics of soil media saturated with salt solutions are constructed based on the concept of the Caputo–Fabrizio fractional derivative. The corresponding boundary-value problems for the system of fractional-differential equations of filtration and salt transfer are posed, the technique for their numerical solution is developed, an approach to the parallelization of computations is presented, and the results of numerical experiments on modeling the dynamics of the process are given. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: boundary-value problems, dynamics of filtration-consolidation processes, finite difference solutions, fractional-differential mathematical models, mathematical modeling, models with non-singular kernel, parallel computing, Boundary value problems, Dynamics, Filtration, Mathematical models, Parallel processing systems, Consolidation process, Finite-difference solution, Fractional derivatives, Fractional differential, Fractional differential equations, Numerical experiments, Numerical solution, Singular kernel, Numerical models

Cite:
Bulavatsky V.M., Bohaienko V.O. (2018). Numerical simulation of fractional-differential filtration-consolidation dynamics within the framework of models with non-singular kernel. Cybernetics and Systems Analysis, 54 (2), 26-37. doi: https://doi.org/10.1007/s10559-018-0020-5 http://jnas.nbuv.gov.ua/article/UJRN-0000846635 [In Russian].