Mathematical Modeling of Solutes Migration under the Conditions of Groundwater Filtration by the Model with the <i>k</i>-Caputo Fractional Derivative
Within the framework of a new mathematical model of convective diffusion with the <i>k</i>-Caputo derivative, we simulate the dynamics of anomalous soluble substances migration under the conditions of two-dimensional steady-state plane-vertical filtration with a free surface. As a corres...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-10-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/2/4/28 |
| _version_ | 1831559670619176960 |
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| author | Vsevolod Bohaienko Volodymyr Bulavatsky |
| author_facet | Vsevolod Bohaienko Volodymyr Bulavatsky |
| author_sort | Vsevolod Bohaienko |
| collection | DOAJ |
| description | Within the framework of a new mathematical model of convective diffusion with the <i>k</i>-Caputo derivative, we simulate the dynamics of anomalous soluble substances migration under the conditions of two-dimensional steady-state plane-vertical filtration with a free surface. As a corresponding filtration scheme, we consider the scheme for the spread of pollution from rivers, canals, or storages of industrial wastes. On the base of a locally one-dimensional finite-difference scheme, we develop a numerical method for obtaining solutions of boundary value problem for fractional differential equation with <i>k</i>-Caputo derivative with respect to the time variable that describes the convective diffusion of salt solution. The results of numerical experiments on modeling the dynamics of the considered process are presented. The results that show an existence of a time lag in the process of diffusion field formation are presented. |
| first_indexed | 2024-12-17T05:32:54Z |
| format | Article |
| id | doaj.art-e2eea335838b425eb4e2cc3f4e25cd77 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-12-17T05:32:54Z |
| publishDate | 2018-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-e2eea335838b425eb4e2cc3f4e25cd772022-12-21T22:01:41ZengMDPI AGFractal and Fractional2504-31102018-10-01242810.3390/fractalfract2040028fractalfract2040028Mathematical Modeling of Solutes Migration under the Conditions of Groundwater Filtration by the Model with the <i>k</i>-Caputo Fractional DerivativeVsevolod Bohaienko0Volodymyr Bulavatsky1VM Glushkov Institute of Cybernetics of NAS of Ukraine, Kyiv 03680, UkraineVM Glushkov Institute of Cybernetics of NAS of Ukraine, Kyiv 03680, UkraineWithin the framework of a new mathematical model of convective diffusion with the <i>k</i>-Caputo derivative, we simulate the dynamics of anomalous soluble substances migration under the conditions of two-dimensional steady-state plane-vertical filtration with a free surface. As a corresponding filtration scheme, we consider the scheme for the spread of pollution from rivers, canals, or storages of industrial wastes. On the base of a locally one-dimensional finite-difference scheme, we develop a numerical method for obtaining solutions of boundary value problem for fractional differential equation with <i>k</i>-Caputo derivative with respect to the time variable that describes the convective diffusion of salt solution. The results of numerical experiments on modeling the dynamics of the considered process are presented. The results that show an existence of a time lag in the process of diffusion field formation are presented.https://www.mdpi.com/2504-3110/2/4/28groundwater filtrationconvective diffusionfractional differential modelk-Caputo derivativefinite-difference scheme |
| spellingShingle | Vsevolod Bohaienko Volodymyr Bulavatsky Mathematical Modeling of Solutes Migration under the Conditions of Groundwater Filtration by the Model with the <i>k</i>-Caputo Fractional Derivative Fractal and Fractional groundwater filtration convective diffusion fractional differential model k-Caputo derivative finite-difference scheme |
| title | Mathematical Modeling of Solutes Migration under the Conditions of Groundwater Filtration by the Model with the <i>k</i>-Caputo Fractional Derivative |
| title_full | Mathematical Modeling of Solutes Migration under the Conditions of Groundwater Filtration by the Model with the <i>k</i>-Caputo Fractional Derivative |
| title_fullStr | Mathematical Modeling of Solutes Migration under the Conditions of Groundwater Filtration by the Model with the <i>k</i>-Caputo Fractional Derivative |
| title_full_unstemmed | Mathematical Modeling of Solutes Migration under the Conditions of Groundwater Filtration by the Model with the <i>k</i>-Caputo Fractional Derivative |
| title_short | Mathematical Modeling of Solutes Migration under the Conditions of Groundwater Filtration by the Model with the <i>k</i>-Caputo Fractional Derivative |
| title_sort | mathematical modeling of solutes migration under the conditions of groundwater filtration by the model with the i k i caputo fractional derivative |
| topic | groundwater filtration convective diffusion fractional differential model k-Caputo derivative finite-difference scheme |
| url | https://www.mdpi.com/2504-3110/2/4/28 |
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