On the behavior of approaches to simulate reactive transport

Two families of approaches exist to simulate reactive transport in groundwa ter: The Direct Substitution Approach (DSA). based on Newton-Raphson and th e Picard or Sequential Iteration Approach (SIA). We applied basic versions of both methods to several test casts and compared both computational deman ds and quality of the solution fur varying grid size. Results showed that t he behavior of the two approaches is sensitive to both grid size and chemis try. As a general rule, the DSA is more robust than the SIA. in the sense t hat 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 he reproduced with fine grids after many iterations when the SIA is used. As a consequence, the DS A runs faster than SIA in chemically difficult cases (i.e.. highly non-line ar 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. mu ch larger for the DSA than for the SIA. so that its CPU time and memory req uirements 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 p roblems. The use of an iterative linear solver for the DSA makes its CPU ti me less sensitive to grid size. (C) 2001 Elsevier Science B.V. All rights r eserved.