Simplified Mathematical Model for the Description of Anomalous Migration of Soluble Substances in Vertical Filtration Flow

• Main Authors: Vsevolod Bohaienko, Volodymyr Bulavatsky
• Format: Article
• Language: English
• Published: MDPI AG 2020-05-01
• Series: Fractal and Fractional
• Subjects: mathematical modeling; migration in porous media; convective diffusion; fractional diffusion equation; mobile–immobile models; simplified models of geomigration
• Online Access: https://www.mdpi.com/2504-3110/4/2/20

Since the use of the fractional-differential mathematical model of anomalous geomigration process based on the MIM (mobile–immoble media) approach in engineering practice significantly complicates simulations, a corresponding simplified mathematical model is constructed. For this model, we state a two-dimensional initial-boundary value problem of convective diffusion of soluble substances under the conditions of vertical steady-state filtration of groundwater with free surface from a reservoir to a coastal drain. To simplify the domain of simulation, we use the technique of transition into the domain of complex flow potential through a conformal mapping. In the case of averaging filtration velocity over the domain of complex flow potential, an analytical solution of the considered problem is obtained. In the general case of a variable filtration velocity, an algorithm has been developed to obtain numerical solutions. The results of process simulation using the presented algorithm shows that the constructed mathematical model can be efficiently used to simplify and accelerate modeling process.