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 Problem
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| Elder's problem was originally derived to describe heat convection, but has been enhanced to include solute transport as well. Here we consider density-driven flow in a porous, homogeneous and fully saturated isotropic medium for a vertical profile with a height of 150 m and a width of 600 m. In the central 300 m of the upper boundary, a seawater boundary condition is applied. We assume that an unlimited supply of salt solution (brine) with a density of 1,200kg/m3 is available. Therefore, the difference in density between the saline solution and the groundwater is 20%. Modelling the problem makes use of the coupled numerical simulation of flow and solute transport. The sides of the aquifer are impermeable, and the simulation is run for 20 years. |
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 Modelling
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| The model area is discretized horizontally by 40 elements and vertically by 25 elements. An element therefore measures 15 m x 6 m. The mesh consists of 1,000 elements and 1,066 nodes.
Atmospheric pressure of 1 bar (105 Pa) is applied to the uper left and right corner of the model. This is implemented by assigning a fixed potential of 150 m as a first-order boundary condition (Dirichlet). The remaining boundaries are no-flow boundaries (second-order boundary condition according to Neumann).
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Results
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The input was modelled for a time period of four years with constant time steps of 0.2 months. The visualization below shows the salt distribution in time, as well as the associated fluid-flow velocities (to be added shortly).
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