A Finite-Difference Approach to the Time-Dependent Mild-Slope Equation  

作　　者：张洪生 赵红军 时钟 

机构地区：[1]School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiao Tong University

出　　处：《China Ocean Engineering》2007年第1期65-76,共12页中国海洋工程（英文版）

基　　金：This work wasjointlysupported by the National Natural Science Foundation of China(Grant No.40106008); the National Natural Science Fundfor Distinguished Young Scholars(Grant No.40225014)

摘　　要：A finite-difference approach is used to develop a time-dependent mild-slope equation incorporating the effects of bottom dissipation and nonlinearity. The Enler predietor-corrector method and the three-point finite-difference method with varying spatial steps are adopted to discretize the time derivatives and the two-dimensional horizontal ones, respectively, thus leading both the time and spatial derivatives to the second-order accuracy. The boundary conditions for the present model are treated on the basis of the general conditions for open and fixed boundaries with an arbitrary reflection coefficient and phase shift. Both the linear and nonlinear versions of the numerical model are applied to the wave propagation and transformation over an elliptic shoal on a sloping beach, respectively, and the linear version is applied to the simulation of wave propagation in a fully open rectangular harbor. From comparison of numerical results with theoretical or experimental ones, it is found that they are in reasonable agreement.A finite-difference approach is used to develop a time-dependent mild-slope equation incorporating the effects of bottom dissipation and nonlinearity. The Enler predietor-corrector method and the three-point finite-difference method with varying spatial steps are adopted to discretize the time derivatives and the two-dimensional horizontal ones, respectively, thus leading both the time and spatial derivatives to the second-order accuracy. The boundary conditions for the present model are treated on the basis of the general conditions for open and fixed boundaries with an arbitrary reflection coefficient and phase shift. Both the linear and nonlinear versions of the numerical model are applied to the wave propagation and transformation over an elliptic shoal on a sloping beach, respectively, and the linear version is applied to the simulation of wave propagation in a fully open rectangular harbor. From comparison of numerical results with theoretical or experimental ones, it is found that they are in reasonable agreement.

关 键 词：TIME-DEPENDENT mild-slope equation finite-difference approach varying steps NONLINEARITY 

分 类 号：P75[天文地球—海洋科学] TU31[建筑科学—结构工程]