Coastal regions are the most densely populated regions of the world. The populations of these regions continue to grow which has created a high demand for water that stresses existing water resources. Coastal aquifers provide a source of water for coastal populations and are generally part of a larger system where freshwater aquifers are hydraulically connected with a saline surface-water body. They are characterized by salinity variations in space and time, sharp freshwater/saltwater interfaces which can lead to dramatic density differences, and complex groundwater chemistry. Mismanagement of coastal aquifers can lead to saltwater intrusion, the displacement of fresh water by saline water in the freshwater regions of the aquifers, making them unusable as a freshwater source. Saltwater intrusion is of significant interest to water resource managers and efficient simulators are needed to assist them. Numerical simulation of saltwater intrusion requires solving a system of flow and transport equations coupled through a density equation of state. The scale of the problem domain, irregular geometry and heterogeneity can require significant computational resources. Also, modeling sharp transition zones and accurate flow velocities pose numerical challenges. Discontinuous Galerkin (DG) finite element methods (FEM) have been shown to be well suited for modeling flow and transport in porous media but a fully coupled DG formulation has not been applied to the variable density flow and transport model. DG methods have many desirable characteristics in the areas of numerical stability, mesh and polynomial approximation adaptivity and the use of non-conforming meshes. These properties are especially desirable when working with complex geometries over large scales and when coupling multi-physics models (e.g. surface water and groundwater flow models). In this dissertation, we investigate a new combined local discontinuous Galerkin (LDG) and non-symmetric, interior penalty Galerkin (NIPG) formulation for the non-linear coupled flow and solute transport equations that model saltwater intrusion. Our main goal is the formulation and numerical implementation of a robust, efficient, tightly-coupled combined LDG/NIPG formulation within the Department of Defense (DoD) Proteus Computational Mechanics Toolkit modeling framework. We conduct an extensive and systematic code and model verification (using established benchmark problems and proven convergence rates) and model validation (using experimental data) to verify accomplishment of this goal. Lastly, we analyze the accuracy and conservation properties of the numerical model. More specifically, we derive an a priori error estimate for the coupled system and conduct a flow/transport model compatibility analysis to prove conservation properties. / text

Storage of freshwater in saline aquifers has a strategic importance in water deficit countries. The freshwater stored in these aquifers may be the only source of water available during times of crisis. Coupled simulation and optimization type groundwater management models have been developed that will achieve the optimal control of the storage of freshwater in a stagnant manner for constant density and variable density flows in hypothetical single- and multi-layered saline aquifers. The study is carried out in two stages. In the first stage, a transient model of five years is simulated that allows sufficient time for the freshwater mound to be created. In the second stage, an optimization model is formulated which minimizes the pumping/injection rates of a set of hydraulic gradient control wells subject to a set of constraints consisting of systems response equations, demand requirements, hydraulic gradient controls, pumping and injection limitations. The optimization models select which wells to be pumped and which ones to be injected and decide on their pumping/injection schedules to maintain the freshwater mound from migration. The results of the optimization models showed that the mound is successfully contained in its original location by controlling the hydraulic gradient via pumping/injection wells.

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Utilizing the analytical solution of the steady state sharp interface saltwater intrusion model in coastal aquifers, a multi-objective optimization formulation of pumping rates and well locations in a coastal aquifer is formulated to solve problems in water management practice. The proposed optimization problem uses progressive genetic algorithm technique and the method developed is applied to the previous work of Cheng et al. [2000]. Through this analysis, several other applications are provided to demonstrate the use of the model in practical applications. This work is the first to optimize pumping rates as well as well locations simultaneously in coastal aquifer management. Known the limitation of the analytical solution, the work is expanded to cover the physics of saltwater intrusion in a more realistic way. This is variable density flow in a variably saturated porous medium. In this method, mixing between two fluids such as saltwater and freshwater can be described and the porous medium is also expanded to cover saturated and unsaturated zones together. One of the objectives is to develop a three dimensional physical model, verify the model, and apply to various applications in coastal aquifers. The developed model, TechFlow, is used to investigate instability issues associated with the numerical solution of the Elder problem in the perspective that includes physical instability issues associated with density differences used in numerical solutions, sensitivity of the solution to idealization irregularity, and the importance of accurate estimation of the velocity field and its association to the grid density levels that is necessary to solve the problem accurately. Saltwater intrusion hydrodynamics in a beach under the influence of tidal effects is also investigated using TechFlow. Based on the results of TechFlow with the use of various boundary conditions for the transport equation, the saltwater intrusion hydrodynamics in a beach under the influence of tidal effects shows unique dynamics. These solutions are primarily affected by density differences, tidal effects on a mild slope, variably saturated porous medium and finite domain solution condition. TechFlow is also used to investigate saltwater upconing beneath pumping wells both two- and three-dimensional applications.