Finite element transport modeling using analytic element flow solutions

Abstract

Finite element methods for solute transport simulation typically use a discrete representation of the flow domain obtained from a finite element solution of the associated groundwater flow problem. Velocity, saturated thickness, and components of the dispersion coefficient tensor are represented as a set of nodal and/or element-averaged values. In contrast, the analytic element method (AEM) provides continuous mesh-independent solutions for these variables. In this paper, a set of techniques for using two-dimensional AEM flow solutions as the basis of finite element solute transport models is introduced. First, a general AEM-based discretization approach is presented that addresses the existence of curved boundaries, singularities, and discontinuities in vertically averaged concentration. Second, residual integration methods that handle continuous parameters with internal and boundary singularities are developed and evaluated. Third, an approach is introduced for handling internal discontinuities in concentration across certain analytic elements. This new approach uses a nonstandard mesh topology and a new formulation for internal coupled boundary conditions. The AEM-based transport simulation methods introduced in this paper are demonstrated to be robust and accurate for a variety of test problems. Copyright 2006 by the American Geophysical Union.