A flux-limiting wetting–drying method for finite-element shallow-water models, with application to the Scheldt Estuary
Gourgue, O.; Comblen, R.; Lambrechts, J.; Kärnä, T.; Legat, V.; Deleersnijder, E. (2009). A flux-limiting wetting–drying method for finite-element shallow-water models, with application to the Scheldt Estuary. Adv. Water Resour. 32(12): 1726-1739. dx.doi.org/10.1016/j.advwatres.2009.09.005
We present a flux-limiting wetting–drying approach for finite-element discretizations of the shallow-water equations using discontinuous linear elements for the elevation. The key ingredient of the method is the use of limiters for generalized nodal fluxes. This method is implemented into the Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM), and is verified against standard test cases. The method is further applied to the wetting and drying of sand banks in the Scheldt Estuary, which is located in northern Belgium and the southern Netherlands. The results obtained for both the benchmarks and the realistic problem illustrate the accuracy of the method in describing the hydrodynamics in the vicinity of dry areas. In particular, the method strictly conserves mass, and there is no transport through dry areas.
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