Finite element methods for variable density flow and solute transport.

*(English)*Zbl 1392.76031Summary: Saltwater intrusion into coastal freshwater aquifers is an ongoing problem that will continue to impact coastal freshwater resources as coastal populations increase. To effectively model saltwater intrusion, the impacts of increased salt content on fluid density must be accounted for to properly model saltwater/freshwater transition zones and sharp interfaces. We present a model for variable density fluid flow and solute transport where a conforming finite element method discretization with a locally conservative velocity post-processing method is used for the flow model and the transport equation is discretized using a variational multiscale stabilized conforming finite element method. This formulation provides a consistent velocity and performs well even in advection-dominated problems that can occur in saltwater intrusion modeling. The physical model is presented as well as the formulation of the numerical model and solution methods. The model is tested against several 2-D and 3-D numerical
and experimental benchmark problems, and the results are presented to verify the code.

##### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

76S05 | Flows in porous media; filtration; seepage |

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

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\textit{T. J. Povich} et al., Comput. Geosci. 17, No. 3, 529--549 (2013; Zbl 1392.76031)

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