Numerical Calculation for Nonlinear Waves in Water of Arbitrarily Varying Depth with Boussinesq Equations  

作　　者：朱良生 洪广文 

机构地区：[1]South China Sea Institute of Oceanology, The Chinese Academy of Sciences [2]Coastal and Ocean Engineering Research Institute, Hohai University

出　　处：《China Ocean Engineering》2001年第3期355-369,共15页中国海洋工程（英文版）

基　　金：This research was financially supported by China National Key Basic Research Project "Circulation Principal and Mathematic Model" (Grant No. 1999043810); Guangdong Science and Technology Innovation Project: "Disaster Diagnoses of Sea Walls" (99B07102G)

摘　　要：Based on the high order nonlinear and dispersive wave equation with a dissipative term, a numerical model for nonlinear waves is developed, It is suitable to calculate wave propagation in water areas with an arbitrarily varying bottom slope and a relative depth h/L(0)less than or equal to1. By the application of the completely implicit stagger grid and central difference algorithm, discrete governing equations are obtained. Although the central difference algorithm of second-order accuracy both in time and space domains is used to yield the difference equations, the order of truncation error in the difference equation is the same as that of the third-order derivatives of the Boussinesq equation. In this paper, the correction to the first-order derivative is made, and the accuracy of the difference equation is improved. The verifications of accuracy show that the results of the numerical model are in good agreement with those of analytical Solutions and physical models.Based on the high order nonlinear and dispersive wave equation with a dissipative term, a numerical model for nonlinear waves is developed, It is suitable to calculate wave propagation in water areas with an arbitrarily varying bottom slope and a relative depth h/L(0)less than or equal to1. By the application of the completely implicit stagger grid and central difference algorithm, discrete governing equations are obtained. Although the central difference algorithm of second-order accuracy both in time and space domains is used to yield the difference equations, the order of truncation error in the difference equation is the same as that of the third-order derivatives of the Boussinesq equation. In this paper, the correction to the first-order derivative is made, and the accuracy of the difference equation is improved. The verifications of accuracy show that the results of the numerical model are in good agreement with those of analytical Solutions and physical models.

关 键 词：nonlinear wave Boussinesq equation arbitrarily varying depth numerical calculation 

分 类 号：O351[理学—流体力学]