The topic of density driven-flow in fractured porous media has long been widely attracted an attention of researchers for coastal environment management and protection. The complex phenomena involved such process are fundamental for seawater intrusion in coastal area, flow through salt formations and saltwater upconing under freshwater lenses. In order to protect the fresh groundwater and the surrounding environment, there is a need to predict the location and the movement of the saltwater interface. The complexity of seawater intrusion problems which generally cannot be analytically solved has risen a high interest on the development of advanced numerical models for density-driven flow as this process is governed by highly coupled, nonlinear, partial differential equations derived from combination of momentum and mass conservation laws.
The objective of this work is to implement, for the first time, the combination of the Mixed Hybrid Finite Element (MHFE) and the Eulerian-Lagrangian Localized Adjoint Method (ELLAM) to solve seawater intrusion problem in fractured porous media.
The MHFE method, which is well known to ensure an accurate and consistent velocity field, and the ELLAM, which is efficient for large time and large scale problem, are coupled to solve the variable-density flow equation. A Discrete Facture Model (DFM) is used to correctly represent fracture embedded in the porous matrix. This model is highly accurate as it can represent fractures explicitly without any simplification. However, numerical solution of this model with classic numerical methods can lead to numerical artifacts that can affect the solution to various degrees and in consequence the physical behavior of the system. This problem can be avoided with our implementation of a high accurate solution based on the Eulerian-Lagrangian Localized Adjoint Method. The performance of our developed model is tested and compared against the Eulerian Discontinuous Galerkin method based on benchmarks inspired from the Henry problem extended to fractured test cases. The results show that ELLAM remains accurate and efficient as this method overcomes the Courant-Friedrichs-Lewy (CFL) restriction.