Shock trains on a planar beach: quasi-analytical and fully numerical solutions

• Published in: Natural hazards (Dordrecht) Vol. 84; no. Suppl 2; pp. 621 - 635
• Main Authors: Soldini, L., Antuono, M., Brocchini, M.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.11.2016; Springer Nature B.V
• Subjects: Beaches; Boundary conditions; Civil Engineering; Computational fluid dynamics; Earth and Environmental Science; Earth Sciences; Environmental Management; Fluids; Geophysics/Geodesy; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Mathematical analysis; Mathematical models; Natural Hazards; Original Paper; Shallow water; Shock waves; Solvers; Water waves; Analytical and numerical solutions; Shock waves; Nonlinear shallow water equations
• ISSN: 0921-030X; 1573-0840
• DOI: 10.1007/s11069-016-2343-8

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.).