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Computation
Volume 14
Issue 4
10.3390/computation14040090
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Two-Dimensional Anomalous Solute Transport in a Two-Zone Fractal Porous Medium

by
B. Kh. Khuzhayorov
1,2,
F. B. Kholliev
3,
A. I. Usmonov
1,4,
B. Rushi Kumar
5 and
K. K. Viswanathan
1,6,*
1
Department of Mathematical Modeling, Faculty of Artificial Intelligence and Digital Technologies, Samarkand State University, 15, University Blvd., Samarkand 140104, Uzbekistan
2
V.I. Romanovsky Institute of Mathematics, Academy of Sciences, Tashken 100174, Uzbekistan
3
Department of Computer and Software Engineering, Faculty of Information Technology, Termez State University, 43, Street Barkamol Avlod, Termez, Surkhandarya Region 190111, Uzbekistan
4
Department of Exact Sciences, Kimyo International University in Tashkent, Tashkent 100121, Uzbekistan
5
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, India
6
Department of Economics and Engineering Sciences, University of Economics and Pedagogy, Karshi 180109, Uzbekistan
*
Author to whom correspondence should be addressed.
Computation 2026, 14(4), 90; https://doi.org/10.3390/computation14040090 (registering DOI)
Submission received: 8 March 2026 / Revised: 27 March 2026 / Accepted: 4 April 2026 / Published: 9 April 2026
(This article belongs to the Section Computational Engineering)
Versions Notes

Abstract

This study addresses a two-dimensional anomalous solute transport process within a two-zone fractal porous medium. A mathematical formulation is developed to characterise transport phenomena in a non-homogeneous porous domain. The medium consists of two interacting regions: one containing mobile fluid and the other containing immobile fluid, between which mass transfer occurs. In the mobile-fluid region, solute transport is governed by the convection–diffusion equation. In contrast, the immobile-fluid region is described using a first-order kinetic model. The problem of solute injection through a designated boundary point is formulated and numerically implemented. The effects of anomalous transport behaviour on solute migration and filtration characteristics are examined. The study further evaluates the pressure field, filtration velocity distribution, and solute concentration in both zones.
Keywords: anomalous Darcy’s law; solute transport; filtration; fractional derivative; pressure; porous medium anomalous Darcy’s law; solute transport; filtration; fractional derivative; pressure; porous medium

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MDPI and ACS Style

Khuzhayorov, B.K.; Kholliev, F.B.; Usmonov, A.I.; Rushi Kumar, B.; Viswanathan, K.K. Two-Dimensional Anomalous Solute Transport in a Two-Zone Fractal Porous Medium. Computation 2026, 14, 90. https://doi.org/10.3390/computation14040090

AMA Style

Khuzhayorov BK, Kholliev FB, Usmonov AI, Rushi Kumar B, Viswanathan KK. Two-Dimensional Anomalous Solute Transport in a Two-Zone Fractal Porous Medium. Computation. 2026; 14(4):90. https://doi.org/10.3390/computation14040090

Chicago/Turabian Style

Khuzhayorov, B. Kh., F. B. Kholliev, A. I. Usmonov, B. Rushi Kumar, and K. K. Viswanathan. 2026. "Two-Dimensional Anomalous Solute Transport in a Two-Zone Fractal Porous Medium" Computation 14, no. 4: 90. https://doi.org/10.3390/computation14040090

APA Style

Khuzhayorov, B. K., Kholliev, F. B., Usmonov, A. I., Rushi Kumar, B., & Viswanathan, K. K. (2026). Two-Dimensional Anomalous Solute Transport in a Two-Zone Fractal Porous Medium. Computation, 14(4), 90. https://doi.org/10.3390/computation14040090

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