Newton-Krylov-multigrid solvers for large-scale, highly heterogeneous, variably saturated flow problems

In this paper, we present a class of solvers developed for the parallel sol ution of Richards' equation, a model used in variably saturated flow simula tions. These solvers take advantage of the fast, robust convergence of glob alized Newton methods as well as the parallel scalability of multigrid prec onditioners. We compare two multigrid methods. The methods differ primarily in their handling of discontinuous and anisotropic permeability fields, wi th one method invoking a simple pointwise smoothing technique and the other a more expensive plane smoother. Computational results are presented to sh ow the effectiveness of the entire nonlinear solution procedure, to demonst rate the effect of discontinuities and anisotropies, and to explore paralle l efficiencies. (C) 2001 Elsevier Science Ltd. All rights reserved.