This research develops a mathematical formulation and numerical solution for the spatial-temporal distribution of groundwater head in heterogeneous porous media. Based on Darcy’s and mass conservation laws, a 3D parabolic partial differential equation for anisotropic aquifers is derived using tensor descriptions. The model incorporates detailed boundary conditions (river interaction, infiltration, evapotranspiration) and satisfies Hadamard criteria for correctness. Heterogeneity is addressed through deterministic and stochastic depth-dependent hydraulic conductivity models. Numerical results are obtained via an explicit finite difference scheme using harmonic mean interface conductivities, verified by von Neumann stability analysis and the CFL condition. The algorithm supports parallel computing on multi-core processors and GPUs. These results are applicable to groundwater resource management, drainage system design, and contaminant transport modeling.
| Mualliflar | Qodirov, R., Boborakhimov, B., Кодиров, Р., Боборахимов, Б. |
|---|---|
| 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 | 2026-05-02 |
| Son | 2 |
| Betlar | 27-41 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.71310/pcam.2_72.2026.03 |
| Indeksga qo‘shilgan | 2026-08-27 |
DOI: 10.71310/pcam.2_72.2026.03 · Maqolaning asl sahifasi
hydrogeology, seepage, mathematical physics, computational mathematics, high-performance computing, гидрогеология, геофильтрация, математическая физика, вычислительная математика, высокопроизводительные вычисления
| APA | Qodirov, R., Boborakhimov, B., Кодиров, Р., & Боборахимов, Б. (2026). Mathematical Model of Groundwater Head Variation Processes in Heterogeneous Porous Media. Ҳисоблаш ва амалий математика муаммолари, (2), 27-41. https://doi.org/10.71310/pcam.2_72.2026.03 |
|---|---|
| GOST (OAK) | Qodirov, R. va b. Mathematical Model of Groundwater Head Variation Processes in Heterogeneous Porous Media // Ҳисоблаш ва амалий математика муаммолари. – 2026. – № 2. – P. 27-41. – DOI: 10.71310/pcam.2_72.2026.03. |
| MLA | Qodirov, R., Boborakhimov, B., Кодиров, Р., and Боборахимов, Б. “Mathematical Model of Groundwater Head Variation Processes in Heterogeneous Porous Media.” Ҳисоблаш ва амалий математика муаммолари, (2), 27-41, 2026. https://doi.org/10.71310/pcam.2_72.2026.03 |
| Chicago | Qodirov, R., Boborakhimov, B., Кодиров, Р., and Боборахимов, Б. “Mathematical Model of Groundwater Head Variation Processes in Heterogeneous Porous Media.” Ҳисоблаш ва амалий математика муаммолари, (2), 27-41 (2026). https://doi.org/10.71310/pcam.2_72.2026.03 |
| Harvard | Qodirov, R., Boborakhimov, B., Кодиров, Р., and Боборахимов, Б (2026) ‘Mathematical Model of Groundwater Head Variation Processes in Heterogeneous Porous Media’, Ҳисоблаш ва амалий математика муаммолари, (2), 27-41. https://doi.org/10.71310/pcam.2_72.2026.03 |
| BibTeX | @article{qodirovr2026,
title = {Mathematical Model of Groundwater Head Variation Processes in Heterogeneous Porous Media},
author = {Qodirov, R. and Boborakhimov, B. and Кодиров, Р. and Боборахимов, Б.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2026},
number = {2},
pages = {27-41},
doi = {10.71310/pcam.2_72.2026.03},
url = {https://doi.org/10.71310/pcam.2_72.2026.03}
} |
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