A comparison of two alternatives to simulate reactive transport in groundwater

Numerical simulation of reactive transport in groundwater (that is, transport of species undergoing chemical reactions) requires the solution of a large number of mathematical equations, which can be highly non linear. This can cause many problems of numerical nature. Therefore, the choice of a method to solve these equations is important. Two types of methods exist: The Direct Substitution Approach (DSA), based on Newton-Raphson, and the Picard or Sequential Iteration Approach (SIA). The advantage of the DSA is that it converges faster and is more robust than the SIA. Its disadvantage is that one has to solve simultaneously a much larger set of equations than for the SIA. We applied both methods to several examples and compared computational behaviour. Results showed that, for chemically difficult (that is, highly non linear) cases, the SIA often requires very small time steps leading to excessive computation times, whereas the DSA does not show this inconvenience due to its robustness. On the other hand, for chemically simple cases but with grids of many nodes, the DSA tends to be less favourable because of the size of the set of equations to be solved.