中文摘要：

针对波浪数值模拟中基于矩形网格的数值方法在深水到浅水的网格间距选择与复杂边界处理上的缺陷,以及基于正交曲线网格和无结构网格的数值方法前处理工作复杂的问题,引入最近在计算力学中发展起来的无网格法——径向点插值法,对经典的双曲型缓坡方程进行空间离散,并在时间上采用四阶Adams-Bashforth-Moulton格式求解建立近岸波浪传播数学模型,通过椭圆形浅滩地形和环形河道的波浪传播计算验证,表明该无网格方法可较为有效地模拟近岸波浪的传播变形,且在处理复杂边界时具有较高的精度。

英文摘要：

Numerical simulation of nearshore waves has become an important topic in coastal dynamics.However,there are certain drawbacks associated with the use of rectangular grids for numerical wave modeling from deep water to shallow water,such as selecting grid resolution and treating complex boundaries.Performing the pre-processing procedure can also be a difficult task to accomplish on an orthogonal curvilinear grid or an unstructured grid.As the result,a radial point interpolation method has been developed recently in computational mechanics.The hyperbolic-type mild-slope equation is used to describe wave propagation in shoaling water.The equation is spatially discretized using the meshless method,and the forth-order Adams-Bashforth-Moulton predictor-corrector scheme is employed to perform time updating.A nearshore wave model is thus obtained.The model is tested in an experimental topography consisting of an elliptic shoal and in a circular channel case.The result shows that the meshless method can effectively simulate the nearshore wave propagation with a satisfactory accuracy.The method can better treat complex boundary conditions.