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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.
We investigate the applicability of the well-known multilevel Monte Carlo (MLMC) method to the class of density-driven flow problems, in particular the problem of salinisation of coastal aquifers. As a test case, we solve the uncertain Henry saltwater intrusion problem. Unknown porosity, permeability and recharge parameters are modelled by using random fields. The classical deterministic Henry problem is non-linear and time-dependent, and can easily take several hours of computing time. Uncertain settings require the solution of multiple realisations of the deterministic problem, and the total computational cost increases drastically. Instead of computing of hundreds random realisations, typically the mean value and the variance are computed. The standard methods such as the Monte Carlo or surrogate-based methods are a good choice, but they compute all stochastic realisations on the same, often, very fine mesh. They also do not balance the stochastic and discretisation errors. These facts motivated us to apply the MLMC method. We demonstrate that by solving the Henry problem on multi-level spatial and temporal meshes, the MLMC method reduces the overall computational and storage costs. To reduce the computing cost further, parallelization is performed in both physical and stochastic spaces. To solve each deterministic scenario, we run the parallel multigrid solver ug4 in a black-box fashion.