高阶Boussinesq型水波方程色散和变浅性能的改进

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。

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

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.