| description abstract | This article presents a two‐dimensional finite element method for the solution of the advection‐dispersion transport equation for multicomponent contaminants. While the approach described is general, the analysis presented here is restricted to nonlinear, equilibrium‐controlled sorption and exchange of soluble inorganic ions. The finite element method is based on a generalization of the one‐dimensional Transport‐Equilibrium Petrov‐Galerkin (TEPG) methods presented by Sheng and Smith [1]. In the TEPG methods, the reaction term is treated as a part of the mass accumulation term. This is in contrast with common formulations where the reaction term is treated as a source term. The transport equation thus contains two unknowns, the aqueous concentration and the total analytical concentration. The solution strategy adopted is to solve the transport equations coupled with chemical equilibrium equations by sequential iteration. No assumption on the reaction term is required when solving the transport equation, which means the transport equation is always conservative. At the end of each time step, both the transport and chemical equilibrium equations are satisfied. To facilitate the solution of the transport equations that may be advection dominated, and optimal upwind weighting procedure and mid‐point time stepping scheme are employed. A number of significant improvements are presented here beyond the TEPG methods presented by Sheng and Smith. These improvements included upwind weighting for a heterogeneous fluid velocity field, the solution of the chemical equilibrium equations for both adsorption and ion exchange, the introduction of an automatic time stepping scheme so as to maintain a predetermined accuracy, and the description of strategies to improve the efficiency of the numerical computations. The TEPG method described is used to analyse several problems with the Peclet number varying between zero and infinity. Both two‐dimensional plane flow and axi‐symmetric problems are considered. The method described is shown to be capable of predicting important qualitative features of advection‐dispersion transport involving nonlinear chemical equilibrium equations. For example problems analyzed, the method is found to be robust, efficient, and accurate, and on the basis of these examples more detailed investigations are justified. | |
