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 |
| Nashr sanasi | 2026-05-02 |
| Son | 2 |
| Betlar | 27-41 |
| Til | Ingliz |
| DOI | 10.71310/pcam.2_72.2026.03 |
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
Recent years have witnessed significant climatic changes and increasing environmental pressure globally, including in Uzbekistan, necessitating an objective regional assessment. This research develops an approach for…
This paper examines a boundary value problem for a degenerate elliptic equation in a planar domain bounded by a line segment and an analytic curve. The primary objective is to construct an explicit analytical solution…
This research presents a multidimensional mathematical model and a robust secondorder numerical algorithm for coupled heat and moisture transfer with pressure-driven gas flow. Utilizing fractional Caputo derivatives (0…
This paper examines the dynamic modes of the fractional Zeeman oscillator. The fractional Zeeman oscillator is a system of two ordinary differential equations with fractional derivatives, understood in the…
This article presents a mathematical model and algorithm for numerically solving a problem for studying the hydrodynamic process of in-situ leaching in a heterogeneous porous medium, taking into account mass transfer…
The discovery of new chemical compounds with specified properties is a challenging problem in drug development. Many studies encode molecules as string representations derived from molecular graphs; however, this…
This article presents a highly accurate and efficient method—a discrete version of the preintegration method—for numerically solving the Cauchy problem for a singularly perturbed third-order equation. The method is…
The solutions of boundary value problems associated with two-parameter singularly perturbed differential equations are well known to exhibit the formation of two distinct boundary layers, typically occurring near the…
This paper considers a two-dimensional linear hyperbolic system with dynamic boundary conditions and proposes a difference scheme for its numerical solution. An explicit–implicit directional splitting method is…
The method of displaced nodes is applied when solving the Dirichlet problem for the Poisson equation in a rectangular domain. By approximating the Laplace operator using moving nodes, we obtain an approximate analytical…