Finite Element Modeling of Saltwater Intrusion Problems with an Application to an Italian Aquifer
Density dependent transport in groundwater may be described by a coupled model of flow and solute transport. The coupling is nonlinear because salt concentration affects the water motion, which in turn controls the fate of the contaminant. For the highest concentrations commonly encountered in the sea (between 25 and 40 kg/m3) the influence of coupling is weak for the flow equation, but stronger for the transport equation. The solution of the algebraic system of nonlinear equations arising front the finite element discretization of the coupled problem may be efficiently obtained by decoupling flow and transport and iterating between the two equations. Using this strategy, at each iteration a linear flow equation and a nonlinear transport equation have to be solved. While for the flow equation the usual finite element approach can be used, linearization techniques have to be employed for the transport equation. The most common solution method uses a Picard linearization applied to the transport equation. however, a more efficient scheme, maned the partial Newton method, can be obtained by substituting the Picard with a Newton type linearization. Titis approach leads to a scheme with better convergence properties but approximately the same computational cost, on a per iteration basis.
Results front two and three-dimensional test simulations show that the partial Newton scheme gives improved convergence and robustness compared to Picard linearization, especially for highly advective problems or large density ratios. The fully three-dimensional finite element model is used to simulate the saltwater contaminations of a coastal aquifer in Southern Italy.
KeywordsTransport Equation Density Ratio Seawater Intrusion Coastal Aquifer Convergence Behavior
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