Parallel simulation of variably saturated soil water flows by fully implicit domain decomposition methods

Abstract

The growing complexity of geometric models for the simulation of subsurface flows leads to the necessity of using the fully implicit method, due to its unconditionally stability with the relaxation of the time step size. In the paper, we introduce and study a parallel and scalable fully implicit solver for the simulation of variably saturated soil water flows. In the proposed approach, the flow problem is discretized in space and time based on a fully implicit, cell-centered finite volume scheme, where several different limiters are applied to guarantee the accuracy of the spatial discretization and an adaptive time-stepping technique for the temporal integration is designed to accelerate the simulation progress. And then the resultant nonlinear algebraic system, arising from the discretization of the variably saturated soil water flows, is solved by a family of Newton–Krylov methods under the domain decomposition framework. Numerical experiments on several standard benchmark tests are used to validate the stability of the fully implicit scheme with large time steps, and to examine the performance of the proposed domain decomposition solver on a parallel computer platform.