Flooding and drying in finiteelement discretizations of shallowwater equations. Part 1: One dimension
Bokhove, O. (2003) Flooding and drying in finiteelement discretizations of shallowwater equations. Part 1: One dimension. [Report]

PDF
1MB 
Abstract:  Free boundaries in shallowwater equations demarcate the timedependent water line between ``flooded'' and ``dry'' topography. A novel numerical algorithm to treat flooding and drying in a formally secondorder explicit space discontinuous finite element discretization of the onedimensional or symmetric shallowwater equations is presented. The algorithm uses fixed Eulerian flooded elements and one mixed EulerianLagrangian element at each free boundary. The positivity of the mean water depth is ensured via a time step restriction based on analysis of a maximum principle for the discretized continuity equation while using an 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 pseudo density (in the shallow water case the depth). It therefore also applies, for example, to space discontinuous finiteelement discretizations of the compressible Euler equations in which vacuum regions emerge, in analogy of the above dry regions. The approach is hypothesized to extend to finitevolume discretizations with similar mean level and slope reconstruction. 
Item Type:  Report 
Additional information:  Imported from MEMORANDA 
Faculty:  Electrical Engineering, Mathematics and Computer Science (EEMCS) 
Research Group:  
Link to this item:  http://purl.utwente.nl/publications/65868 
Export this item as:  BibTeX EndNote HTML Citation Reference Manager 
Repository Staff Only: item control page