On the behavior of approaches to simulate reactive transport

Two families of approaches exist to simulate reactive transport in groundwater: The Direct Substitution Approach (DSA), based on Newton-Raphson and the Picard or Sequential Iteration Approach (SIA). We applied basic versions of both methods to several test cases and compared both computational demands and quality of the solution for varying grid size. Results showed that the behavior of the two approaches is sensitive to both grid size and chemistry. As a general rule, the DSA is more robust than the SIA, in the sense that its convergence is less sensitive to time step size (any approach will converge given a sufficiently small time step). Moreover, the DSA leads to a better simulation of sharp fronts, which can only be reproduced with fine grids after many iterations when the SIA is used. As a consequence, the DSA runs faster than SIA in chemically difficult cases (i.e., highly non-linear and/or very retarded), because the SIA may require very small time steps to converge. On the other hand, the size of the system of equations is much larger for the DSA than for the SIA, so that its CPU time and memory requirements tend to be less favorable with increasing grid size. As a result, the SIA may become faster than the DSA for very large, chemically simple problems. The use of an iterative linear solver for the DSA makes its CPU time less sensitive to grid size.