An Analytic Element Method solution for simulating multiple steady-state groundwater contamination scenarios

This paper presents a new Analytic Element Method (AEM) model for a 2D reactive transport problem. The AEM approach offers domain complexity due to superposition of multiple boundary conditions, while minimizing computational efforts, being a grid-free method. For the solution development, transformations of the advection–dispersion–reaction (ADR) equation are applied resulting in an equivalent mathematical problem governed by the modified Helmholtz equation. A solution (infinite series of Mathieu functions) derived for circular source elements provides the steady-state concentration distribution of two compounds undergoing an instantaneous and binary reaction in uniform flow. The solution is verified with an absolute error of the order $10^{-7}$ mg/l and a relative error of order $10^{-4}$ along boundary conditions. A sensitivity analysis identifies source strength and utilization factor of the reactants as parameters with the strongest impact on the plume length. The practicality of the developed AEM model is illustrated using different conceptual scenarios in which multiple source elements are superimposed as co- and counter interacting sources. Additionally, the method of images is applied using the same solution for representing the vertically oriented domain. These highlight the potential of the developed model for simulating a variety of practical conditions, such as irregular source geometries with or without continuity with unrestricted domain extent and minimal computational effort. Further, three field sites are briefly evaluated to present the applicability of the model.