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Numerical Simulations for Saltwater Intrusion by the Mixed Hybrid Finite Element Method and Discontinuous Finite Element Method

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Abstract

The proposed numerical code simulates the displacement of two miscible fluids through a saturated porous medium (2D configuration). Coupling between flow and transport is carried out by an equation of state. In the mixing zone, the density is assumed to vary as a function of concentration. The model uses a combination of the mixed hybrid finite element method and the discontinuous finite element method.

Applied in its classical development, the mixed hybrid finite element method leads to a non-conservative formulation of the mass balance equation. However, one of the main reasons for using this technique is the ability to conserve mass cell-by-cell. Consequently, a new formulation that makes it possible to hold the conservative form of the continuity equation and so preserve the mass cell-wise is proposed. Although the pertinence of these approaches could have also been tested on other standard benchmarks, e.g., Elder's problem or salt dome problem, we have voluntarily limited ourselves to Henry's problem (1964). This choice was dictated by the possibility of a comparison with a semi-analytical solution. Contrary to previous numerical results, the comparison is made for the whole mixing zone. The very good agreement between our results and the semi-analytical solution shows the robustness and the efficiency of this approach for the seawater intrusion problems.

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  1. Laboratoire Environnement, Géomécanique et Ouvrages, École Nationale Supérieure de Géologie – Institut National Polytechnique de Lorraine, Rue du Doyen Marcel Roubault, BP 40, F-54501, Vandæuvre-lès-Nancy

    M. A. Buès & C. Oltean

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  1. M. A. Buès
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  2. C. Oltean
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Buès, M.A., Oltean, C. Numerical Simulations for Saltwater Intrusion by the Mixed Hybrid Finite Element Method and Discontinuous Finite Element Method. Transport in Porous Media 40, 171–200 (2000). https://doi.org/10.1023/A:1006626230029

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