Cybernetics and Systems Analysis

, Volume 54, Issue 2, pp 193–204 | Cite as

Numerical Simulation of Fractional-Differential Filtration-Consolidation Dynamics Within the Framework of Models with Non-Singular Kernel

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Abstract

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.

Keywords

mathematical modeling dynamics of filtration-consolidation processes fractional-differential mathematical models models with non-singular kernel boundary-value problems finite difference solutions parallel computing 
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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine

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