波浪产生和运动的二阶计算模型

Wave generation and propagation in a second-order wave model

在快速模拟波浪运动的谱方法基础上,引入造波边界,建立了模拟波浪产生和运动的二阶计算模型。采用摄动展开方法简化了带有造波边界的水波运动问题,将速度势分解,得到了满足造波边界和自由面边界的速度势的一般解,运用快速Fourier变换和时间积分,建立了模拟波浪产生和运动的数学模型。基于该模型,采用不同的数值造波条件,模拟了波浪的产生问题;考虑了波浪的初始运动问题;通过把数值结果与物理实验的比较,验证了波浪计算模型的有效性。

A second-order wave model is derived for the wave generation and propagation, based on the spectral expansion.A boundary-value problem, for the generation of water wave by a wavemaker, is simplified by decomposing the total velocity into two parts, and two efficient solutions are achieved for the wavemaker problem and the free surface problem. The system,corrected up to a second order in the wave steep, is then solved by applying spectral expansions based on Fast Fourier Transform. We study the evolution of generated waves using different wavemaker inputs and compare the computations with the analytical solutions. The initial evolution of the generated waves is also considered. In order to validate our numerical scheme, laboratory experiments are carried out and a reasonable agreement is observed between experimental data and numerical results.