一般曲线坐标系下波浪传播的数值模拟
Numerical simulation model of wave propagation in curvilinear coordinates
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摘要: 在曲线坐标系下,建立了缓变水深水域波浪传播的数值模拟模型.模型适宜于复杂变化的边界形状,克服了各种代数坐标变换的局限性.在建立模型时,将原始的椭圆型缓坡方程的近似型式——依赖时间变化的抛物型方程,作为控制方程,既克服了一般抛物近似方法的缺点,又便利了方程的求解;从开边界条件、不同反射特性的固壁边界条件相统一的表达式出发,对边界条件进行处理;用ADI法数值求解控制方程.对模型的验证表明,数值解与物模实验值吻合良好,模型对于具有复杂边界的工程实际有较强的适应性.Abstract: In the curvilinear coordinates, a numerical simulation model for wave propagation in water of slowly varying topography is presented.The model is suitable to complicated loundary shapes and overcomes the limitation of other models with algorithm transfomtation.In the model, the time-dependent parabolic equation, deduced from the original elliptic type of mild-slope equation, is used as the governing equation.The present governing equation not only avoids the drawback to common parabolic form of mild-slope equation but also is convenient for solution.Based on the general conditions for open and fixed natural boundaries with an arbitrary reflection coefficient and phase shift, the boundary conditions for the present model are treated.The alternative direction implicit method is used to solve the governing equation.The numerical results of the present model are in agreement with those of physical models.Systematical tests show that the present model can reasonably simulate the wave transformation, such as shoaling, refraction, diffraction and reflection.So the present model is able to be used in coastal engineering with complicated boundary shapes extensively.
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BERKHOFF J C W. Computation of combined refraction-diffraction[A]. Proc 13th Conference on Coastal Engineering[C], Vol. 1. Vancouver, Canada:ASCE, 1972.471-490. PANCHANG V G, PEARCE B R. Solution of the mild-slope wave problem by iteration[J]. Applied Ocean Research,1991, 13(4):187-199. BERKHOFF J C W, BOOIJ N, RADDER A C. Verification of numerical wave propagation models for simple harmonic water waves[J]. Coastal Engineering, 1982, 6:255-279. PANCHANG V G, CHSHMAN-ROISIN B, PEARCE B R. Combined refraction-diffraction of short-waves in large coastal regions[J]. Coastal Engineering, 1988, 12:133-156. RADDER A C. On the parabolic equation method for water-wave propagation[J]. Journal of Fluid Mechanics, 1979, 95:159-176. LI Bin. ANASTASIOU K. Efficient elliptic solvers for the mild slope equation using the multigrid technique[J]. Coastal Engineering, 1992, 16:245-266. LI Bin. An evolution equation for water waves[J]. Coastal Engineering, 1994,23:227-242. 陶建华,韩光,龙文.浅水区大面积波浪场数值计算方法的研究[A].第九界全国海岸工程学术讨论会论文集[C]北京:海洋出版社,1999.17-24. COPELAND G J M. A practical alternative to the "mild-slope" wave equation[J]. Coastal Engineering, 1985, 9:125-149. EBERSOLE B A. Refraction-diffraction model for linear water waves[J]. Journal of Waterway, Port, Coastal and Ocean Enginnering, 1985, 111(6):939-953. 张洪生.近岸水域波浪传播的数学模型[R].上海:华东师范大学,2002. 洪广文,冯卫兵,夏期颐,等.缓变水深和流场水域波浪折射、绕射数值模拟[A].第八届全国海岸工程学术讨论会论文集(下)[C].北京:海洋出版社,1997.703-714. 洪广文,冯卫兵,张洪生.海岸河口水域波浪传播数值模拟[J].河海大学学报,1999,27(2):1-9. LIUPLF, BOLSSEVAINPL. Wave propagation between two breakwaters[J]. Journal of Waterway, Port, Coastaland Ocean Engineering, 1988, 114(2):237-247. XU Bing-yi, PANCHANG V, DEMIRBILEK Z. Exterior reflections in elliptic harbor wave models[J]. Journal of Waterway, Port, Coastal and Ocean Engineering, 1996, 122(3):118-126. KIRBY J T, DALRYMPLE R A, KABU H. Parabolic approximation for water waves in conformal coordinate systems[J].Coastal Engineering, 1994, 23:185-213. ZHANG Hong-sheng, HONG Guang-wen, DING Ping-xing. Numerical simulation of nonlinear wave propagation in water of mildly varying topography with complicated boundary[J]. China Ocean Engineering, 2001, 15(1):37-52. HONG Gnang-wen. Mathematical models for combined refraction-diffraction of waves on non-uniform current and depth[J]. China Ocean Engineering, 1996, 10(4):433-454. PAN Jun-ning, ZUO Qi-hua, WANG Hong-chuan. Efficient numerical solution of the modified mild-slope equation[J].China Ocean Engineering, 2000, 14(2):161-174. BRACKBILL J U, SALTZMAN J S. Adaptive zoning for singular problems in two dimensions[J]. Journal of Computation Physics, 1982,46:342-368. 曾平.适应性坐标变换在天然河道平面计算中的应用[J].水动力研究与进展(A辑),1991,6(增刊):100-107. 史峰岩,孔亚珍,丁平兴潮滩海域边界适应网格潮流数值模型[J]海洋工程,1998,16(3):68-75. 刘卓,曾庆存.自适应网格在大气海洋问题中的初步应用[J].大气科学,1994,18(6):641-648 张洪生.有限水深非线性船行波的数值模拟[D].南京:河海大学,1991. 张洪生.非线性波传播的数值模拟[D].南京:河海大学,2000 HONG Guang-wen, ZHANG Hong-sheng, FENG Wei-bing. Numerical simulation of nonlinear three-dimensional waves in water of arbitrary varying topngraphy[J]. China Ocean Engineering, 1998, 12(4):383-404. ISOBE M. A parabolic refraction-diffraction equation in the ray-front coordinate system[A]. Proceedings 20th International Coastal Engineering Conference, Taipei:ASCE, 1986.306-317. MEMOS C D. Water waves diffracted by two breakwaters[J]. Journal of Hydraulic Research, 1980, 18(4):343-357.
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