A mathematical and numerical model is presented for the process of liquid solution filtration in a cylindrical porous filter. The model is based on the Brinkman-Darcy equations, describing fluid motion in a porous medium with porosity and permeability linked through the Kozeny-Carman relation. The transport of dissolved substances is governed by the advection-diffusion-reaction system, complemented by the LDF kinetics and the Langmuir isotherm for adsorption. The model also incorporates a clogging (colmatation) equation that accounts for particle deposition and temporal reduction of filter porosity. A finite-difference numerical algorithm with iterative pressure correction using the conjugate gradient method is developed, ensuring stability according to the Courant-Friedrichs-Lewy criterion. The proposed approach enables analysis of the coupled hydrodynamic, mass transfer, and adsorption phenomena, allowing for assessment of filtration efficiency and prediction of filter lifespan in liquid purification systems.
| Mualliflar | Ravshanov, N., Boborahimov, B.I., Berdiyorov, Sh.Sh., Равшанов, Н., Боборахимов, Б.И., Бердиёров, Ш.Ш. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashriyot | Тошкент ахборот технологиялари университети қошидаги, Ахборот-коммуникация технологиялари илмий-инновацион, маркази |
| ISSN | 2181-8460, 2181-046X |
| Nashr sanasi | 2025-11-16 |
| Son | 5 |
| Betlar | 49-63 |
| Til | Ingliz |
| DOI | 10.71310/pcam.5_69.2025.04 |
| Indeksga qo‘shilgan | 2026-08-27 |
DOI: 10.71310/pcam.5_69.2025.04 · Maqolaning asl sahifasi
hydrodynamics of porous media, mass transport, Brinkman-Darcy equations, numerical approximation, liquid purification, гидродинамика пористых сред, перенос массы, уравнения Бринкмана-Дарси, численная аппроксимация, очистка жидких сред
| APA | Ravshanov, N., Boborahimov, B.I., Berdiyorov, Sh.Sh., Равшанов, Н., Боборахимов, Б.И., & Бердиёров, Ш.Ш. (2025). Numerical Modeling of Liquid Solution Filtration in a Cylindrical Porous Filter. Ҳисоблаш ва амалий математика муаммолари, (5), 49-63. https://doi.org/10.71310/pcam.5_69.2025.04 |
|---|---|
| GOST (OAK) | Ravshanov, N. va b. Numerical Modeling of Liquid Solution Filtration in a Cylindrical Porous Filter // Ҳисоблаш ва амалий математика муаммолари. – 2025. – № 5. – P. 49-63. – DOI: 10.71310/pcam.5_69.2025.04. |
| MLA | Ravshanov, N., Boborahimov, B.I., Berdiyorov, Sh.Sh., Равшанов, Н., Боборахимов, Б.И., and Бердиёров, Ш.Ш. “Numerical Modeling of Liquid Solution Filtration in a Cylindrical Porous Filter.” Ҳисоблаш ва амалий математика муаммолари, (5), 49-63, 2025. https://doi.org/10.71310/pcam.5_69.2025.04 |
| Chicago | Ravshanov, N., Boborahimov, B.I., Berdiyorov, Sh.Sh., Равшанов, Н., Боборахимов, Б.И., and Бердиёров, Ш.Ш. “Numerical Modeling of Liquid Solution Filtration in a Cylindrical Porous Filter.” Ҳисоблаш ва амалий математика муаммолари, (5), 49-63 (2025). https://doi.org/10.71310/pcam.5_69.2025.04 |
| Harvard | Ravshanov, N., Boborahimov, B.I., Berdiyorov, Sh.Sh., Равшанов, Н., Боборахимов, Б.И., and Бердиёров, Ш.Ш (2025) ‘Numerical Modeling of Liquid Solution Filtration in a Cylindrical Porous Filter’, Ҳисоблаш ва амалий математика муаммолари, (5), 49-63. https://doi.org/10.71310/pcam.5_69.2025.04 |
| BibTeX | @article{ravshanovn2025,
title = {Numerical Modeling of Liquid Solution Filtration in a Cylindrical Porous Filter},
author = {Ravshanov, N. and Boborahimov, B.I. and Berdiyorov, Sh.Sh. and Равшанов, Н. and Боборахимов, Б.И. and Бердиёров, Ш.Ш.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2025},
number = {5},
pages = {49-63},
doi = {10.71310/pcam.5_69.2025.04},
url = {https://doi.org/10.71310/pcam.5_69.2025.04}
} |
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