A Curvilinear Finite Element Model for Simulating Two‐Well Tracer Tests and Transport in Stratified Aquifers

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The problem of solute transport in steady nonuniform flow created by a recharging and discharging well pair is investigated. Numerical difficulties encountered with the standard Galerkin formulation in Cartesian coordinates are illustrated. An improved finite element solution strategy is presented to overcome the numerical problem. The strategy is based on a formulation performed in three‐dimensional curvilinear coordinates. This formulation is developed especially for the simulation of two‐well injection‐withdrawal tracer tests conducted in homogeneous or stratified aquifers. The formulation can also be applied to other types of problems involving transport in homogeneous and stratified aquifers. A three‐dimensional finite element approximation is derived by two successive applications of upstream weighted‐residual and subdomain collocation procedures. First, the weighted residual procedure is formulated in the horizontal flow plane using curvilinear coordinates along and normal to streamlines. Upstream weighting is included but automatically controlled and limited to one dimension along the main flow direction. Second, the subdomain collocation procedure is formulated in the vertical dimension. Spatial discretization of the three‐dimensional flow region is performed using a curvilinear finite element mesh that is point‐centered in the horizontal plane and block‐centered in the vertical direction. General algorithms are developed for mesh generation, time stepping and matrix reduction. The solution algorithm is designed to accommodate several thousand nodal unknowns with minimal core storage and CPU time requirement. Two simulation examples are presented to verify and validate the numerical model in two dimensions using an analytical solution and experimental laboratory and field data. A comparative study shows that the proposed formulation is superior to the standard Galerkin formulation in Cartesian coordinates both in terms of accuracy and computational efficiency. The field simulation example indicates the need to conduct a more elaborate three‐dimensional simulation study allowing for vertical variation in hydraulic conductivity. Such a study has been completed and is reported in the follow‐up paper of this series.