Modeling variable-density flow in saturated-unsaturated porous media: An advanced numerical model

• Published in: Advances in water resources Vol. 159; p. 104077
• Main Authors: Younes, Anis, Koohbor, Behshad, Belfort, Benjamin, Ackerer, Philippe, Doummar, Joanna, Fahs, Marwan
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2022; Elsevier
• Subjects: climate change; Discontinuous finite element method; Earth Sciences; equations; Field simulation; finite element analysis; Lebanon; mathematical models; Method of lines; Mixed finite element method; Multi-point flux approximation; saltwater intrusion; saturated flow; Sciences of the Universe; Unsaturated flow; Variable-density flow; viscosity; water; Lebanon; Mixed finite element method; Discontinuous finite element method; Method of lines; Variable-density flow; Field simulation; Unsaturated flow; Multi-point flux approximation; Discontinuous finite element
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2021.104077

•An advanced model is developed for variable density flow in unsaturated media.•Sophisticated methods for spatial and temporal discretizations are combined.•Performance of the new model are shown against standard strategies in COMSOL.•SWI under climate change stresses is simulated in an unconfined aquifer in Lebanon.•Due to its robustness, the model is suitable for sustainable resources management. Modeling variable-density flow in unconfined aquifers is a challenging task because of the nonlinear coupling between variably saturated flow and contaminant transport. This results in a highly nonlinear system since the strongly nonlinear Richards flow equation is, in addition, coupled to the advection-dispersion transport equation by viscosity and density variation. The solution of such a nonlinear system is often subject to convergence issues and can be very expansive in terms of computational time, especially for large-scale problems. Conventional numerical algorithms based on the sequential approach and the classical finite difference or finite element methods with the first-order backward Euler time integration scheme are generally inefficient and/or do not provide satisfactory results. In this work, we develop a new efficient and accurate 2D numerical model for the transport of dense contaminants in unsaturated porous media that allows for the simulation of large-scale problems. This research describes a new model that combines advanced spatial discretization methods (mixed hybrid finite element method, discontinuous Galerkin finite element method, and multipoint flux approximation method) with higher-order time integration techniques via the method of lines (MOL). The latter allows one to adapt the time step's size and the order of the time integration to improve the computational efficiency while maintaining accuracy. The robustness and accuracy of the new model are shown by comparison against a widely used commercial code based on the standard finite element method. The applicability of the developed model to a large-scale problem is then investigated by simulating saltwater intrusion under a climate change projection and long-term pumping regimes for the Akkar coastal aquifer in Lebanon using a simplified 2D conceptual model.