Groundwater modelling: Towards an estimation of the acceleration factors of iterative methods via an analysis of the transmissivity spatial variability

When running a groundwater flow model, a recurrent and seemingly subsidiary question arises at the starting step of computations: what value of acceleration parameter do we need to optimize the numerical solver? A method is proposed to provide a practical estimate of the optimal acceleration parameter via a geostatistical analysis of the spatial variability of the logarithm of the transmissivity field Y. The background of the approach is illustrated on the successive over-relaxation method (SOR) used, either as a stand-alone solver, or as a symmetric preconditioner (SSOR) to the gradient conjugate method, or as a smoother in multigrid methods. It shows that this optimum acceleration factor is a function of the standard deviation and the correlation length of Y. This provides an easy-to-use heuristic procedure to estimate the acceleration factors, which could even be incorporated in the software package. A case study illustrates the steps needed to perform this estimation.