Abstract
This study, part of the Special Issue dedicated to the 70th anniversary of Professor Efim Pelinovsky, focuses on a topic that has been central in Professor Pelinovsky’s research, i.e. the analytical and numerical modelling of shallow water waves. We specifically focus on the evolution of trains of shock waves on a planar beach. Antuono (J Fluid Mech 658:166–187, 2011) has, for the first time, proposed a quasi-analytical solution for a train of shock waves forced by a constant Riemann invariant. The present contribution clarifies the validity of such solution and its value for benchmarking nonlinear shallow water equation solvers. Hence, the same tests of Antuono (J Fluid Mech 658:166–187, 2011) have been run by means of the solver of Brocchini et al. (Coast Eng 43(2):105–129, 2001) revealing surprisingly and reassuring good agreements. This provides significant support to the mentioned analytical solution and allows to critically analyse the eventual discrepancies, due to the practicalities of running numerical shallow water solutions (e.g. influence of the boundary conditions, of the numerical resolution, etc.).
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Acknowledgments
This work has been funded by the Flagship Project RITMARE—the Italian Research for the Sea—coordinated by the Italian National Research Council and funded by the Italian Ministry of Education, University and Research within the National Research Program 2011. Support from the EsCoSed Project, financed by the US-ONR through the NICOP Research Grant (N62909-13-1-N020), is gratefully acknowledged.
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Soldini, L., Antuono, M. & Brocchini, M. Shock trains on a planar beach: quasi-analytical and fully numerical solutions. Nat Hazards 84 (Suppl 2), 621–635 (2016). https://doi.org/10.1007/s11069-016-2343-8
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DOI: https://doi.org/10.1007/s11069-016-2343-8