On Solving Groundwater Flow and Transport Models with Algebraic Multigrid Preconditioning

Iterative solvers preconditioned with algebraic multigrid have been devised as an optimal technology to speed up the response of large sparse linear systems. In this work, this technique was implemented in the framework of the dual delineation approach. This involves a single groundwater flow linear solution and a pure advective transport solution with different right-hand sides. The new solver was compared with other preconditioned iterative methods, the MODFLOW's GMG solver, and direct sparse solvers. Test problems include two- and three-dimensional benchmarks spanning homogeneous and highly heterogeneous and anisotropic formations. For the groundwater flow problems, using the algebraic multigrid preconditioning speeds up the numerical solution by one to two orders of magnitude. The algebraic multigrid preconditioner efficiency was preserved for the three dimensional heterogeneous and anisotropic problem unlike for the MODFLOW's GMG solver. Contrarily, a sparse direct solver was the most efficient for the pure advective transport processes such as the forward travel time simulations. Hence, the best sparse solver for the more general advection-dispersion transport equation is likely to be Péclet number dependent. When equipped with the best solvers, processing multimillion grid blocks by the dual delineation approach is a matter of seconds. This paves the way for its routine application to large geological models. The paper gives practical hints on the strategies and conditions under which algebraic multigrid preconditioning would remain competitive for the class of nonlinear and/or transient problems.