The Dual Formulation of Flow for Contaminant Transport Modeling: 1. Review of Theory and Accuracy Aspects

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Abstract
Steady state groundwater flow systems can be described by means of either potentials or stream functions. If the objective is the definition of migration paths and the identification of hydrogeologic parameters in the context of a contaminant transport study, stream functions can give results that are both more useful and more accurate than those obtained with potentials alone. In this paper the dual theory that links potentials and stream functions is reviewed with a focus on physical relevance in practical situations, and a dual finite element solution is developed. Advantages of the dual method, including the ease with which advective transport components can be evaluated, are discussed. It is shown by means of an example that the stream function solution can give superior accuracy in the definition of the velocity field required for transport simulations. A companion paper deals with a case study.