关于采用高阶Boussinesq方程求解波浪散射问题的注记

A Note on Numerical Solution of Water Wave Scattering Problems over a Trench by High Order Boussinesq Equations

本文讨论了采用高阶Boussinesq方程模拟波浪散射时对基本速度变量位置的局部光滑处理方法。通过光滑局部基本速度变量的取值深度,减小其高阶导数项的量值、加快级数收敛速度进而改善模型方程求解深水波浪散射问题的能力。对于底部边界具有一阶导数不连续的情况,通过局部光滑,可以将基本速度变量取值深度尖角转化为圆角过渡,从而改善速度分布。对于其它任意变化的底部边界,为了减少高阶底坡导数项的影响,在曲率和高阶底坡导数项与斜率具有相同量级的情况下亦需要对基本速度变量的取值深度局部光滑。数值计算结果表明本文提出的光滑技术可以很好地改善Boussinesq方程模拟浅水波和深水波在斜坡地形上散射问题的能力。

The water wave scattering by two dimensional trenches was studied by using the Boussinesq equations based on the utility velocity variables at the water level of half depth. To reduce the value of high order derivative terms relating to the water depth, the local smoothing technique was introduced. The performance on the water wave scattering problem in deep water region could be improved by smoothing the local relative water depth of utility velocity variables. To plane slope trenches, the local smoothing technique can improve the performance of the wave model in deep water region. To general vary beaches, the local smoothing can help to reduce the magnitude of curvature and higher order derivatives of water depth. The numerical results present that the correct estimations of the scattering on trenches for waves from shallow to deep water can be obtained by solving the modified Boussinesq equations associated with proper local smoothing technique.