A New Numerical Method Based on Discontinuous Galerkin for Simulation of Seawater Intrusion into Coastal Aquifers

Background and objectives : Coastal aquifers are of the most important freshwater resources in many countries, especially in arid and semi arid zones. Due to the proximity and contact with the sea, and thus the threat of contamination because of the seawater intrusion, management and protection of these freshwater resources are quite necessary. Therefore, the main goal of the present study is to develop a new numerical model for simulation of the contaminant transport in coastal aquifers (seawater intrusion into coastal aquifers) using discontinuous Galerkin method.
Materials and methods : In this study, Discontinuous Galerkin methods which have been less developed in engineering problems were applied for discretization of the coupled nonlinear system of flow and solute transport equations in a saturated porous medium and a fully implicit backward Euler scheme was applied for temporal discretization. The primal DGs have been developed successfully for density dependent flows by applying initial and boundary conditions to the coupled equations. Then, to linearize the resulting nonlinear systems, Picard iterative technique was applied and Chavent Jaffre slope limiter was used to eliminate the nonphysical oscillations appeared in the solution. Note that the formulation which was used is based on the equivalent freshwater head and normalized mass fraction as dependent variables.
Results: Five benchmark problems including standard Henry problem together with its two modified versions, Elder problem and Goswami Clement experimental problem in three distinct phases were simulated for validation and verification of the numerical code. For all the benchmark problems, the results were compared against other solutions in order to assess the model accuracy. The solution convergence was proved for the standard henry problem. Applying the Chavent Jaffre slope limiter to the experimental test showed a satisfactory results obtained from the simulations. In comparison with other numerical solutions, the present model revealed a good accuracy for all the problems.
Conclusion: The DG model were verified and evaluated using the above-mentioned problems. The results from simulations showed a good accuracy for DG method. In portions of the domain where the velocity is high, it was indicated that the DG methods in comparison with other numerical methods e.g. finite difference, do not emerge non-physical oscillations. Also, the results show a less numerical dispersion in comparison with other numerical methods such as finite volume methods. In addition, simulating the experimental problem with the current model shows the practical aspects of the developed model based on discontinuous Galerkin.