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

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.