| A Finite-Difference Approach to the Time-Dependent Mild-Slope Equation |
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| 作者姓名： | 张洪生 赵红军 时钟 |
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| 作者单位： | School of Naval Architecture Ocean and Civil Engineering，Shanghai Jiao Tong University，School of Naval Architecture，Ocean and Civil Engineering，Shanghai Jiao Tong University，School of Naval Architecture，Ocean and Civil Engineering，Shanghai Jiao Tong University，Shanghai 200030，China，Shanghai 200030，China，The College of Traffic and Ocean Engineering，Hohai University，Nanjing 210098，China，Shanghai 200030，China |
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| 基金项目： | 国家自然科学基金;国家自然科学基金 |
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| 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 Euler predictor-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.
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| 关 键 词： | 时变缓底坡波动方程 有限差分法 非线性 椭圆偏微分方程 |
| 收稿时间： | 2006-08-08 |
| 修稿时间： | 2006-11-30 |
A Finite-Difference Approach to the Time-Dependent Mild-Slope Equation |
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| ZHANG Hong-sheng,ZHAO Hong-jun,SHI Zhong.A Finite-Difference Approach to the Time-Dependent Mild-Slope Equation[J].China Ocean Engineering,2007,21(1):65-76. |
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| Authors: | ZHANG Hong-sheng ZHAO Hong-jun SHI Zhong |
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| Abstract: | A finite-difference approach is used to develop a time-dependent mild-slope equation incorporating the effects of bottom dissipation and nonlinearity.The Euler predictor-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. |
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| Keywords: | time-dependent mild-slope equation finite-difference approach varying steps nonlinearity |
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