This work examines the effect of asymptotic dispersion for different contaminants, like heavy metals, biological, and radiological types, in heterogeneous groundwater systems. The migration of contaminants within groundwater systems is controlled by advection, dispersion, and sorption phenomena, and these mechanisms are mathematically modeled using the Advection-Dispersion Equation (ADE). Using the Thomas algorithm, a numerical simulation with the Peaceman - Rachford Alternating Direction Implicit (PR-ADI) scheme is applied to solve the ADE under the directional injection boundary (axial input sources). The study on asymptotic dispersion coefficients revealed a broader plume evolution. Non-linear sorption models depended on the saturation limit, and various parameters revealed physically relevant results. The iso-concentration figures depict flow patterns for diverse directional hydrological inflows, supporting stability interpretations. This study introduces a computational approach for modeling contaminant transport in groundwater systems, emphasizing asymptotic field conditions that introduce heterogeneity, coupled with nonlinear sorption effects on the plume morphology. The results highlight how plume morphology responds to variable dispersion and velocity, offering guidance for field-scale aquifer analysis and water quality management. The study is also aligned with Sustainable Development Goal 6 - Clean water and sanitation.
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