Computer modeling of the dynamics of migration processes of soluble substances in the case of groundwater filtration with free surface on the base of the fractional derivative approach
DOI:
https://doi.org/10.15407/dopovidi2018.12.021Keywords:
dynamics of convective and diffusive processes, finite-difference solutions, fractional differential mathematical models, generalized Caputo—Gerasimov derivative, mathematical and computer modeling, non-linear boundary-value problems, steady state flat-vertical groundwater filtrationAbstract
The mathematical modeling of the fractional differential dynamics of the process of anomalous convective diffusion of soluble substances is conducted for the case of flat-vertical steady state groundwater filtration with free surface. Within the framework of the model with a generalized Caputo—Gerasimov fractional derivative, the corresponding non-linear boundary-value problem is posed, a finite-difference method for its approximated solution is given, and the results of computer experiments are described.
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