# zbMATH — the first resource for mathematics

Conservative 1D-2D coupled numerical strategies applied to river flooding: the Tiber (Rome). (English) Zbl 1452.76126
Summary: Coupled 1D-2D numerical strategies are presented in this work for their application to fast computation of large rivers flooding. Both 1D and 2D models are built using explicit upwind finite volume schemes, able to deal with wetting-drying fronts. The topography representation is described via cross sections for the 1D model and with quadrilateral/triangular structured/unstructured meshes for the 2D model. The coupling strategies, free of hydraulic structures and tuning parameters, are firstly validated in a laboratory test dealing with a levee break and its flooding into a lateral plane. The numerical results are compared with a fully 2D model as well as with measurements in some gauge points giving satisfactory results. The simulation of a real flooding scenario in the Tiber river near the urban area of Rome (Italy) is then performed. A lateral coupling configuration is provided, in which the flood wave propagation in the main channel is simulated by means of a 1D model and the inundation of the riverside is simulated by means of a 2D model. On the other hand, a frontal coupling, in which the flood wave is simulated in a 1D model first and then it is propagated into a 2D model, is also performed. The flooding extension is almost well captured by all the schemes presented, being the 1D-2D lateral configuration the most confident with speed-ups of around $$15\times$$.

##### MSC:
 76M12 Finite volume methods applied to problems in fluid mechanics 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 86A05 Hydrology, hydrography, oceanography
##### Keywords:
1D-2D coupled model; shallow water; conservation; river flooding
Full Text: