A numerical model preserving nontrivial steady-state solutions for predicting waves run-up on coastal areas

TL;DR

This paper introduces a novel numerical model based on the Saint-Venant system that accurately predicts wave propagation and run-up on coastlines by preserving nontrivial steady-state solutions, validated against laboratory experiments.

Contribution

The paper presents a new finite volume numerical scheme that preserves nontrivial steady states for wave modeling in coastal areas, improving accuracy over existing methods.

Findings

The model accurately predicts wave run-up on sloping beaches.

Numerical results agree well with laboratory experiments.

The scheme maintains steady-state solutions without numerical artifacts.

Abstract

In this study, a numerical model preserving a class of nontrivial steady-state solutions is proposed to predict waves propagation and waves run-up on coastal zones. The numerical model is based on the Saint-Venant system with source terms due to variable bottom topography and bed friction effects. The resulting nonlinear system is solved using a Godunov-type finite volume method on unstructured triangular grids. A special piecewise linear reconstruction of the solution is implemented with a correction technique to ensure the accuracy of the method and the positivity of the computed water depth. Efficient semi-implicit techniques for the friction terms and a well-balanced formulation for the bottom topography are used to exactly preserve stationary steady-state s solutions. Moreover, we prove that the numerical scheme 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 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.