Abstract Groundwater contaminant modeling presents several challenges to the mathematician. Among these are the need to compute accurate water velocities and difficulties arising from fine-scale heterogeneities and sharp concentration fronts. This paper presents parallelizable numerical methods that address these challenges.
For groundwater flow, mixed finite-element models yield velocities comparable in accuracy to computed heads. However, large variations in hydraulic conductivity can cause iterative matrix solvers to converge slowly. The fine grids needed to resolve heterogeneities aggravate the poor conditioning. A parallelizable, multigrid-based iterative scheme for the lowest-order mixed method largely overcomes both sources of poor behavior.
For contaminant transport, finite-element collocation yields high-order spatial accuracy. The timestepping scheme combines a modified method of characteristics, which reduces temporal errors when advection dominates, with an alternating-direction formulation, which is "embarrassingly parallel" and has a favorable operation count.
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