A proposed upstream weight numerical method for simulating pollutant transport in groundwater

An alternative upstream weighting numerical method is proposed to simulate the transport process in groundwater under a variety of conditions. The discretized system of the solute transport equations is derived from the integral form that expresses the balance of mass in each element. An upstream weight that depends on the local Peclet number is directly added to the basis functions. When convective transport dominates the dispersive transport, this technique can eliminate the oscillation of solutions efficiently, with only a nominal increase of computation effort over that of the general linear triangular Galerkin finite element method. The accuracy of the proposed numerical model is tested against two classical problems for which analytical solutions exist. The agreement is nearly exact. An additional numerical example is used to illustrate the applicability of this model.