简便推导改进Boussinesq方程的一种方法

Boussinesq方程的推导有多种方法,其中最简便的方法由Beji和Nadaoka提出.利用该方法,从传统的Boussinesq方程出发,通过引用2个参数来改善方程的色散性,并通过与Schaffer和Madsen的模型对比给出这2个参数,使得波浪的变浅作用性能得以改善,同时方程的适用水深提高近1倍.在建立的模型基础上,利用Crank-Nicolson格式的有限差分法对方程进行了数值计算.数值结果与实验数据吻合较好,验证了本文的数值模型.

A simple method for deriving improved Boussinesq equations

There are many ways to derive Boussinesq equations, one of the simple methods was proposed by Beji and Nadaoka. Based on the classical Boussinesq equations, the simple method is used with two parameters employed to improve the linear dispersion of the Boussinesq equations. Also by the comparison with the model derived by Schaffer and Madsen, the two parameters are obtained, which improve the linear shoaling characteristics, and the applicable water depth is increased by nearly one time. Based on the model, the Crank-Nicolson finite difference scheme is used to calculate the numerical value of the model. The numerical results are then compared with the experimental data and there is a good agreement, which demonstrates the validation of the model.