标题： 非定常波浪在单向变化地形上传播的缓坡方程边界元公式 显示英文标题

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

摘要： 本文提出了一种边界元公式，用于解决一维变水深波浪传播问题中的缓坡方程。 基于Belibassakis \cite{Belibassakis2000}提出的格林函数近似，开发了一个完整的基本解核，并与边界元方案相结合，用于解决在闭合和开放域中水波传播问题，其中地形在优选方向上任意且平滑变化。 通过求解一些示例问题，展示了所提出公式的准确性，这些问题考虑了任意几何形状和坡度高达1:3的可变海底剖面。 获得的结果还与理论解进行了比较，显示出极好的一致性，证明了其潜力。 显示英文摘要

摘要： 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.