An Upstream Weight Multiple‐Cell Balance Finite‐Element Method for Solving Three‐Dimensional Convection‐Dispersion Equations

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Abstract
An upstream weight multiple‐cell balance finite‐element method is developed to simulate the three‐dimensional contaminant transport in aquifers. The method combines the concepts of local mass balance and finite‐element approximations. When convective transport dominates the dispersive transport, the proposed technique effectively eliminates the oscillation of numerical solutions with only a nominal increase of formulation effort over that of the general Galerkin finite‐element method. Two numerical examples for which analytical solutions exist are used to verify the proposed numerical solutions. An additional example is presented to demonstrate the practical applicability of the proposed method.

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