Discretization of analytic element flow solutions for transport modeling

The 2D analytic element method (AEM) is an alternative to finite difference methods for simulating steady-state unconfined groundwater systems. AEM is commonly used for capture zone delineation, but has not yet been used as a basis for contaminant transport simulation. However, the analytic element method is a promising source of flow information in that it is independent of any grid, and thus suitable for developing less constrictive reactive transport discretizations. One of the reasons AEM has never been used in this capacity is that most conventional contaminant transport simulation algorithms are based upon discrete finite difference flow solutions, whereas AEM represents the flow variables needed for transport as continuous functions of space. While it is adequate to numerically integrate cell-averaged saturated thickness values for use in transport simulations, discretizing system fluxes is a more demanding process. Eulerian transport algorithms require local (cell-by-cell) mass balance of water for both accuracy and stability. While the analytic element method provides exceptionally precise globally and locally conservative results, simply interpolating the analytic functions that describe flux in AEM is not adequate for obtaining mass-conservative interfacial fluxes. Likewise, the vector geometry of the analytic element method makes it challenging to accurately distribute the various sink and source terms to grid cells. This includes terms for the influence of leakage and recharge, which may also be represented as continuous functions of space. The following paper presents a suite of algorithms used to properly translate the continuous aquifer fluxes and vector-based source and sink fluxes into a format amenable to finite-difference-based transport simulation.