Boundary element formulation of the Mild-Slope Equation for harmonic water waves propagating over unidirectional variable bathymetries

TL;DR

This paper introduces a boundary element method for solving the Mild-Slope Equation to model water wave propagation over variable bathymetries, accurately capturing phenomena like refraction and shoaling in complex geometries.

Contribution

It develops a new boundary element formulation based on Green's function approximation for efficient wave modeling over unidirectional variable bathymetries.

Findings

Accurately models wave refraction, reflection, diffraction, and shoaling.

Demonstrates excellent agreement with theoretical solutions.

Handles arbitrary geometries with slopes up to 1:3.

Abstract

This paper presents a boundary element formulation for the solution of the Mild-Slope equation in wave propagation problems with variable water depth in one direction. Based on the Green's function approximation proposed by Belibassakis \cite{Belibassakis2000}, a complete fundamental-solution kernel is developed and combined with a boundary element scheme for the solution of water wave propagation problems in closed and open domains where the bathymetry changes arbitrarily and smoothly in a preferential direction. The ability of the proposed formulation to accurately represent wave phenomena like refraction, reflection, diffraction and shoaling, is demonstrated with the solution of some example problems, in which arbitrary geometries and variable seabed profiles with slopes up to 1:3 are considered. The obtained results are also compared with theoretical solutions, showing an excellent agreement that demonstrates its potential.