高阶Boussinesq型水波方程色散和变浅性能的改进  

Improvement of dispersion and shoaling property of a set of high-order Boussinesq-type equations

作　　者：张振伟 刘必劲 邹志利[3] 傅丹娟 ZHANG Zhenwei;LIU Bijin;ZOU Zhili;FU Danjuan(School of Civil Engineering and Architecture,Xiamen University of Technology,Xiamen 361024,China;Hainan Institute of Zhejiang University,Sanya 572025,China;State Key Laboratory of Coastal and Offshore Engineering,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]厦门理工学院土木工程与建筑学院,福建厦门361024 [2]海南浙江大学研究院,海南三亚572025 [3]大连理工大学海岸和近海工程国家重点实验室,辽宁大连116024

出　　处：《河海大学学报（自然科学版）》2022年第2期37-44,共8页Journal of Hohai University(Natural Sciences)

基　　金：国家自然科学基金(51879033);2020年厦门市青年创新基金(3502Z20206069)。

摘　　要：在无因次水深为6.28条件下,为了优化方程色散参数,将一组高阶Boussinesq型方程的相速度与线性波相速度之间误差平方累计之和最小,而后根据变浅分析确定变浅参数,进一步分析了不同参数对高阶Boussinesq型方程的色散和变浅性能的影响。针对该组高阶Boussinesq型方程,基于非交错网格构建了时间差分格式为混合4阶Adam-Bashforth-Moulton的数值模型,利用数值模型计算了波浪在潜堤上的传播演化,结果表明采用优化参数的计算结果与试验数据符合更好。The linear dispersion and shoaling coefficients of a set of high-order Boussinesq-type equations are optimized,which significantly improves the linear dispersion and linear shoaling performance of the original equations.The sum of error squares between the phase velocity of the high-order Boussinesq-type equations and the linear wave phase velocity is minimized to optimize the dispersion coefficients of the equation for kh=6.28,with k as the wave number and h as the water depth.The shoaling coefficients are determined according to the linear shoaling analysis.The linear dispersion and shoaling performance of the Boussinessq-type equations with different sets of coefficients is presented.A numerical model with a time difference format of mixed fourth-order Adam-Bashforth-Moulton is constructed based on non-staggered grid.The numerical model is applied to simulate the wave propagation and evolution on the submerged breakwater,and the simulation results using the optimized coefficients proposed by present work are in much better agreement with the experimental data.

关 键 词：BOUSSINESQ型方程 线性色散 线性变浅 数值模型 

分 类 号：P731.2[天文地球—海洋科学]