A numerical model for predicting waves run-up on coastal areas

Abstract

ABSTRACT In this study, numerical investigations are performed to validate a numerical model for the prediction of waves propagation and waves run-up on coastal zones. The proposed numerical model is based on the depth-averaged two-dimensional dispersive shallow water equations with source terms due to variable bottom topography and bed friction effects. We propose to solve the resulting nonlinear system using a well-balanced positivity preserving Godunov-type finite volume method on unstructured triangular grids. We used a semi-implicit scheme for the friction terms and a well-balanced formulation for the bottom topography. Moreover, we prove that the numerical scheme exactly preserves a class of nontrivial steady-state solutions. To validate the proposed numerical model against experiments, we first demonstrate its ability to preserve nontrivial steady-state solutions over a slanted surface and then we model several laboratory experiments for the prediction of waves run-up on sloping beaches. The numerical simulations are in good agreement with laboratory experiments which confirms the robustness and accuracy of the proposed numerical model in predicting waves propagation on coastal areas.