Abstract
An optimal upstream weighting is proposed in the multiple cell balance solutions of solute transports in groundwater to eliminate oscillation and minimize numerical dispersion. The optimal upstream weighting is directly added to the basis function. The optimal values of upstream weighting coefficients numerically obtained depend not only on the mesh Peclet number but also on the flow patterns. When convective transport dominates dispersive transport or when pumping wells provoke a converging flow field, this upstream weighting technique is efficient to eliminate the oscillations of solutions. The accuracy of the proposed numerical method is tested against a classical problem whose analytical solutions exist. The comparison between the numerical results and the analytical solutions demonstrates the possibility of a real gain in precision using the proposed optimal weighting method. A more concrete numerical example is carried out to illustrate the applicability of the proposed model.
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