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 solution of Richardsʹ equation, a model used in variably saturated flow simulations. These solvers take advantage of the fast, robust convergence of globalized Newton methods as well as the parallel scalability of multigrid preconditioners. We compare two multigrid methods. The methods differ primarily in their handling of discontinuous and anisotropic permeability fields, with one method invoking a simple pointwise smoothing technique and the other a more expensive plane smoother. Computational results are presented to show the effectiveness of the entire nonlinear solution procedure, to demonstrate the effect of discontinuities and anisotropies, and to explore parallel efficiencies.