NUMERICAL MODELING AND OPTIMIZATION OF GROUNDWATER FILTRATION PROCESSES USING COMPUTATIONAL ALGORITHMS

Abstract

This study develops a reproducible computational framework for groundwater flow simulation and constrained abstraction planning. A conservative finite-volume scheme with harmonic interface transmissivity and backward Euler integration represents transient flow in a heterogeneous confined aquifer. Linear response coefficients connect the numerical model to a convex quadratic allocation problem. A controlled 90-day experiment distributes a demand of 1,200 m³/day among three abstraction zones. Compared with equal allocation, the nominal optimum reduces mean squared drawdown by 25.87% and maximum drawdown by 30.88%, while preserving the total supply. A 20% conductivity reduction exposes a small violation of the hydraulic-head constraint; explicit scenario constraints remove this violation. Additional experiments quantify the effects of a prescribed head buffer and the maximum feasible abstraction under the stated boundaries. Analytical benchmarks, mesh refinement, an independent linear solver and water-balance checks support numerical consistency. The results demonstrate the computational mechanism under synthetic conditions and define the field information needed before practical application.