Numerical Solution of the Problem of Anomalous Solute Transport in a Two-Dimensional Nonhomogeneous Porous Medium

Numerical Solution of the Problem of Anomalous Solute Transport in a Two-Dimensional Nonhomogeneous Porous Medium

J.M.Makhmudov^{1, a)}., A.I.Usmonov^1,b)., Z.D.Kaytarov^1,c)., B.Sultonov^2,d).

¹Samarkand State University

²Chirchik State Pedagogical Institute.
^a) [e-mail];

^bв) Corresponding author: [e-mail];

^c) [e-mail]

Abstract. The process of anomalous solute transport in a two-dimensional porous medium is modeled by differential equations with a fractional derivative. The problem of the solute transport is formulated and numerically solved both with and without taking into account the anomalous properties of the transfer. The anomaly of the solute transport is taken into account in the form of a fractional derivative with respect to spatial coordinates in the diffusion terms of the transfer equations. It is believed that the transfer anomaly is associated with the fractal structure of the medium. The exponential and sinusoidal forms of changes in the filtration rate and hydrodynamic dispersion over time are considered. It has been determined that the fractionality of the derivatives in the diffusion term leads to "fast diffusion".