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1 前言 波浪运动相当复杂,波浪受地形和水工建筑物的影响,产生浅水变形、折射、绕射、反射等现象,准确模拟有相当的难度,因而波浪数学模型是水动力数学模型中难度较大的数学模型. 波浪数学模型的研究开始于60年代,法国的Biesel最早提出采用积分方程的波浪数学模型,70年代,荷兰的Berkhoff提出了缓坡方程波浪数学模型,丹麦的Abbott提出了Boussinesq方程波浪数学模型,缓坡方程和Boussinesq方程的提出,是波浪数学模型的发展的重要里程碑.80年代以来,欧美和日本学者在缓坡方程和Boussinesq方程的基础上,对波浪数学模型进行完善和发展,将这些模型用于研究不规则波的传播,并考虑波浪的非线性影响、底摩损耗以及波浪与水流的相互作用等,波浪数学模型作为波浪运动研究的新方法与水工物理模型相互补充成为海岸工程波浪问题研究的有力工具. 我们对波浪数学模型的研究分两个阶段进行,1996～1997年初为研究的第一阶段,该阶段参考丹麦水工所Abbott、Mc Cowan和Madsen等人1990年前的所有公开发表的论文,全面了解经典波浪数学模型的发展过程.对经典波浪数学模型的基本原理、高精度差分方法和消波边界处理等问题有了深入的认识.1997年初完成了经典波浪数学模型的建立与
1 Introduction Wave movement is quite complicated. Waves are affected by topography and hydraulic structures, resulting in deformation, refraction, diffraction and reflection of shallow water. It is quite difficult to accurately simulate the waves. Therefore, the wave mathematical model is difficult in the hydrodynamic mathematical model A large mathematical model.Wave mathematical model of the study began in the 60’s, France’s Biesel earliest wave equation using integral equations mathematical model, the 70’s, Berkhoff Holland proposed gentle slope equation wave mathematical model, Danish Abbott proposed Boussinesq equation wave Mathematical models, gentle slope equations and Boussinesq equations are important milestones in the development of wave mathematical models.Early 1980s, European, American and Japanese scholars improved and developed wave mathematical models based on the gentle slope equations and the Boussinesq equations. These mathematical models, The model is used to study the propagation of irregular waves and take into account the nonlinear effects of waves, the loss of bottom friction and the interaction between wave and water. The mathematical models of waves are complementary to the hydraulic physical model as a new method of wave motion research and become a marine engineering A powerful tool for wave research. Our mathematical model of waves The study was conducted in two phases. From 1996 to early 1997, the first phase of the study, which referenced all published papers prior to 1990 by the Abbott, Mc Cowan, and Madsen et al. Of the Danish Hydraulics, provided a comprehensive understanding of the classical wave mathematical model The development of classical wave mathematical model of the basic principles of high-precision differential method and the elimination of wave boundary treatment and other issues have in-depth understanding of the early 1997 completed the establishment of classical mathematical model and wave