River floods can be simulated with the 2D shallow water system of equations using finite volume methods, where the terrain is discretized in cells that form the computational mesh. Usually a proper treatment of wet/dry fronts is required. River levees can be modelled as part of the topography by means of sufficiently small cells of higher elevation than the rest of the bed level in locally refined meshes. This procedure is associated with a large computational time since the time step depends directly on the cell size. The alternative proposed in this work includes the levees as internal boundary conditions in the 2D numerical scheme. In particular, levees have been defined by a weir law that, depending on the relative values of water surface levels on both sides, can formulate the discharge for different situations (i.e. free flow and submerged flow). In addition, having identified numerical difficulties in cases of low discharge under free flow conditions, a novel procedure to avoid oscillations has been developed and called volume transport method. The validation and comparison between methods has been carried out with benchmark test cases and, in addition, with a real flood event in the Ebro River (Spain)
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This work was partially funded by the MINECO/FEDER under research Project CGL2015-66114-R and by Diputacion General de Aragon, DGA, through Fondo Europeo de Desarrollo Regional, FEDER. The third author also wants to thank to the MINECO for his Research Grant DI-14-06987.
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Echeverribar, I., Morales-Hernández, M., Brufau, P. et al. Use of internal boundary conditions for levees representation: application to river flood management. Environ Fluid Mech 19, 1253–1271 (2019). https://doi.org/10.1007/s10652-018-09658-6
- Internal boundary condition
- Finite volume
- River flooding
- Numerical modelling