The Applicability of Dispersive and Nondispersive Wave Models for Description of Long Wave Propagation and Run-Up on a Beach


Ahmed Abdalazeez
Department of Marine Systems, Tallinn University of Technology, Akadeemia tee 15A, Tallinn 12618, Estonia
Denys Dutykh
Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LAMA, 73000 Chambéry, France
Petr Denissenko
School of Engineering, University of Warwick, Coventry, UK
Ira Didenkulova
Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Minin str. 24, Nizhny Novgorod 603950, Russia.


The aim of this work is to study the applicability of dispersive and nondispersive wave models for description of long wave propagation and run-up on a beach in the case of constant bottom depth merged with the beach of constant slope. Numerical simulations are performed in the framework of two models: (1) non-dispersive model, based on the Nonlinear Shallow Water (NSW) theory and (2) weakly dispersive model in the Boussinesq approximation, based on the modified Peregrine system. Both models use the finite-volume method with the second-order UNO2 reconstruction in space and the third-order Runge–Kutta scheme with locally adaptive time steps. Both models also include a Manning friction term to take into account for friction effects on the sloping beach.

April 12, 2020