Flooding and drying in discontinuous Galerking finite element discretizations of shallow-water equations. Part 1: One dimension.

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Bokhove, Onno (2005) Flooding and drying in discontinuous Galerking finite element discretizations of shallow-water equations. Part 1: One dimension. Journal of Scientific Computing, 22-23 (1-3). pp. 47-82. ISSN 0885-7474

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Abstract:Free boundaries in shallow-water equations demarcate the time-dependent water line between "flooded" and "dry" regions. We present a novel numerical algorithm to treat flooding and drying in a formally second-order explicit space discontinuous Galerkin finite-element discretization of the one-dimensional or symmetric shallow-water equations. The algorithm uses fixed Eulerian flooded elements and a mixed Eulerian–Lagrangian element at each free boundary. When the time step is suitably restricted, we show that the mean water depth is positive. This time-step restriction is based on an analysis of the discretized continuity equation while using the HLLC flux. The algorithm and its implementation are tested in comparison with a large and relevant suite of known exact solutions. The essence of the flooding and drying algorithm pivots around the analysis of a continuity equation with a fluid velocity and a pseudodensity (in the shallow water case the depth). It therefore also applies, for example, to space discontinuous Galerkin finite-element discretizations of the compressible Euler equations in which vacuum regions emerge, in analogy of the above dry regions. We believe that the approach presented can be extended to finite-volume discretizations with similar mean level and slope reconstruction.
Item Type:Article
Copyright:© 2005 Springer
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/61963
Official URL:http://dx.doi.org/10.1007/s10915-004-4136-6
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