三维Boussinesq型水波方程的改进

良好的色散性和变浅性是Boussinesq水波数值模型能够精确模拟水波问题的重要前提，针对一组最高空间导数为2的三维Boussinesq型水波方程（Liu等，2018）在色散性和变浅性的不足，重新引入带有不同色散参数和变浅参数的计算速度表达式，得到了新的三维Boussinesq型方程。对该方程进行理论分析，以相关解析解为参考，分析了新参数下方程的相速度、和差频和变浅梯度等方面性能。理论分析结果表明：方程的综合性能有了较大改善，验证了改进的理论有效性。进一步，为验证改进方程的数值有效性，建立了基于混合4阶Adams-Bashforth-Moulton格式的时间差分数值模型。数值模拟了波浪在潜堤上的传播变形过程，将计算波面位移与Luth等（1994）的试验数据进行了比较，结果表明，与改进前相比，改进后计算结果与试验结果的吻合程度更高。

The improvement of a 3D Boussinesq-type model for water waves

High accuracy in both dispersion and shoaling property of a Boussinesq-type model is the fundamental basis for accurate water wave simulations.To amend the deficiency of dispersion and shoaling of a set of three-dimensional Boussinesq-type equations for water waves with the highest spatial derivative of 2 (Liu et al., 2018), the computational velocity expressions with different dispersion parameters and shoaling parameters are introduced, and a new Boussinesq-type model is obtained. The phase celerity, super- and sub-harmonics and shoaling gradient of the present model are analyzed. The theoretical analysis results show that comprehensive performance of the model has been greatly improved, which verifies the effectiveness of the improved method. Furthermore, to verify the validity of the numerical model, the numerical model is solved by Finite Difference Method with a composite fourth-order Adams-Bashforth-Moulton scheme for time integration. Numerical simulations are carried out upon regular wave propagation and deformation process over a submerged breakwater, the simulated surface elevations are compared with the related experimental data measured by Luth et al.(1994). The results show that the improved numerical model is in better agreement with the measurements than the model with original parameters.