On Solving Groundwater Flow and Transport Models with Algebraic Multigrid Preconditioning

01/16/2020
by   M. A. Sbai, et al.
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Sparse iterative solvers preconditioned with the algebraic multigrid has been devised as an optimal technology to speed up the response of large linear systems. In this work, this technique was introduced into the framework of the dual delineation approach. This involves a single groundwater flow solution and a scalar advective transport solution with different right-hand sides. The method was compared with traditional preconditioned iterative methods and a direct sparse solver on several two- and three-dimensional benchmarks spanning homogeneous and heterogeneous formations. The algebraic multigrid preconditioning enabled speedups lying between one and two orders of magnitude for the groundwater flow problems. However, the sparse direct solver was the fastest for the pure advective transport processes such as the forward travel time simulations. This leads to conclude that the best sparse solver for the general advection-dispersion transport equation is Péclet number dependent. When equipped with the best solvers, the dual delineation technique was run on a took only a few seconds to solve multi-million grid cell problems paving the way for comprehensive sensitivity analysis. The paper gives practical hints on the strategies and conditions under which the algebraic multigrid preconditioning for nonlinear and/or transient problems would remain competitive.

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