非线性抛物型缓坡方程的数值模拟

参考Lo对MNLS方程中非线性项的处理方法,但不转换到频域求解,同时采用Li修正的非线性弥散关系,对非线性抛物型缓坡方程在复数域进行数值模拟,并分别在Berkhoff椭圆地形及淹没圆形浅滩地形验证了该模型,得到了较好的结果。此模型可以有效地模拟非线性波浪问题。此非线性项的处理方法使得数值计算过程中不需迭代求解,同时减少了边界周期性的限制,易于操作编程,提高了计算效率。

Numerical simulation of the nonlinear parabolic mild-slope equation

The nonlinear parabolic mild-slope equation with the dispersive relation, which Li had modified, was numerically simulated over the complex field. The numerical method doesn't need transform the function to spectral-domain. This is different from that Lo used to simulate the MNLS equation with the nonlinear items. The authors simulated the surface water wave under both the Berkhoff elliptic topography and the circular shoal topography with the model, and the solution coincide quite well with that have been. The model is effective to simulate nonlinear water wave. This method to solve the nonlinear items is very useful and easy to implement. It can solve the equation without iteration and the limit of the periodic boundary.