摘要
在邹志利(2005)推导的二阶Boussinesq水波方程基础上,利用改变两个参数值,使得方程的相速度和群速度在水深等于中等水深时的误差减小。传统方法确定Boussinesq水波方程时给出的参数值是利用线性Stokes色散关系式的Padè二阶逼近来确定参数值,这使得方程的色散精度有所降低,对此文章给出合理的解释。利用线性多步法中的4阶预报和4阶校正的格式对方程进行了数值计算。针对波浪在潜堤上和椭圆型浅滩的传播变形进行了数值模拟,改变系数后的数值模拟结果与实验结果吻合更好,验证了系数的合理改变是对方程色散精度的进一步修正这一结论。
Based on the Boussienseq equations derived by Zou（2005）, a slight modification of the value of parameters enables the model to be accurate in linear dispersion properties. The traditional way of determining the value of the parameters will decrease the accuracy of the wave phase speed and wave group speed when comparing the linear dispersion expression of the Boussinesq model with the second Pade expansion of the linear Stokes dispersion expression, about which, a proper explanation is given in this paper. Fourth-order predict and fourth order correct scheme of linear multi-layers steps are utilized to solve the present model. Numerical simulations of wave propagation over a submerged bar and over an ellipse shoal are carried out, From the comparisons among present results, original results and the experimental results, the agreement of the present model is much better, which proves the conclusions that properly selected parameters will improve the linear dispersion properties.
出处
《水运工程》
北大核心
2008年第8期1-5,共5页
Port & Waterway Engineering
关键词
水波方程
色散性
Padè二阶展开
线性多步法
Boussinesq equations
dispersion property
second order Pade expansion
linear multi -step
