Modelling three dimensional groundwater flow and transport by hexahedral finite elements.
Résumé
This research work deals with three-dimensional modeling of groundwater flow and solute transport problems in groundwater aquifer systems, with several complexities, heterogeneities and variable conditions as encountered in the field. Finite element methods are used throughout to solve a range of different problems, using in particular the Galerkin weighted residual approach based on trilinear hexahedral elements. Special emphasis is made on transient and non-linear groundwater flow problems with moving interfaces, such as the water table and the freshwater-saltwater sharp interface. A generalized Fast Updating Procedure technique is developed for these situations, which presents a number of advantageous features in comparison to classic computational techniques used to deal with such problems. One of the important contributions is the automatic construction of the generic soils characteristic curves, which are dynamically dependent upon the overall system water status. Several test examples are successfully worked out for validating this technique in different aquifer configurations, and under different initial and boundary conditions. These test cases show that the proposed method is cheap, numerically stable and accurate. Numerical stability is guaranteed through a developed solver, which is obtained by using state of the art methods for robust preconditioning and efficient numerical implementation. The accuracy is demonstrated by comparison against analytical, other numerical approaches, and laboratory experimental solutions. The usefulness of the method is clearly shown by the application of the 3-D sharp interface finite element model 'GEO-SWIM' to the coastal aquifer system of Martil in the north of Morocco. Several efficient runs are made, leading to a calibrated management model for the study area, giving a clear picture of the salinization risk in the aquifer due to saltwater encroachment. Three-dimensional modeling of solute transport problems in groundwater aquifer systems is equally investigated. It is concluded that the standard Galerkin finite element method is computationally intensive, since the obtained system of numerical equations is very large, sparse, none symmetric and usually difficult to solve with standard iterative techniques. Hence, preconditioning is necessary to improve the convergence behavior of ill-conditioned systems. In this work, we propose an M-matrix type of transformation on the general transport matrix which guarantees the existence of the preconditioning schemes, and hence improves the overall solvers performance and robustness. The usefulness of the method is demonstrated by solving several test examples with different complexities, including hypothetical and field applications in Belgium. Different solvers are tested as the minimal residual method and the stabilized biconjugate gradient method, in combination with different preconditioning schemes, as diagonal scaling and incomplete factorization. It is concluded that M-matrix preconditioning is very simple to implement, and proves to be very efficient and robust. An effort is put on packaging the computer programs, by giving modern visual support to many modules. Therefore, several GUI programs are provided as complementary tools to support the developed models, enabling their friendly use, and the possibility for future extensions.
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