Center for Scientific Computing (CSC)
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A 3d regional density-driven flow model of a heterogeneous aquifer system at the German North Sea Coast is set up within the joint project NAWAK (“Development of sustainable adaption strategies for the water supply and distribution infrastructure on condition of climatic and demographic change”). The development of the freshwater-saltwater interface is simulated for three climate and demographic scenarios.
Groundwater flow simulations are performed with the finite volume code d3f++ (distributed density driven flow) that has been developed with a view to the modelling of large, complex, strongly density-influenced aquifer systems over long time periods.
Far outside the surface of slabs, the exact exchange (EXX) potential vx falls off as −1/z , if z denotes the direction perpendicular to the surface and the slab is localized around z=0 . Similarly, the EXX energy density ex behaves as −n/(2z) , where n is the electron density. Here, an alternative proof of these relations is given, in which the Coulomb singularity in the EXX energy is treated in a particularly careful fashion. This new approach allows the derivation of the next-to-leading order contributions to the asymptotic vx and ex . It turns out that in both cases, the corrections are proportional to 1/z2 in general.