Mass balance errors when solving the convective form of the transport equation in transient flow problems

The original (divergence) form of the solute transport equation expresses the mass balance of solutes in groundwater. The alternative (convective) form can be obtained by subtracting the flow equation, multiplied by concentration, from the original form. Many investigators prefer the latter because it facilitates the use of Lagrangian or mixed Eulerian-Lagrangian numerical methods for solution. However, it performs very poorly in transient contaminant transport problems with large temporal variations in water content. We propose an alternative to overcome this difficulty. It consists of evaluating the water content at time level k + 1 - eta if concentration in the convective term is evaluated at time level k + eta. For this reason we have called it reverse time weighting, whereas we call an evaluation of the water content at time level k + eta straight time weighting. We show that reverse time weighting improves significantly over straight time weighting not only in terms of mass balance errors, but also in terms of concentration errors.