Application of higher-level GN theory to some wave transformation problems
Application of higher-level GN theory to some wave transformation problems
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更高层次的GN理论在一些波动变换问题中的应用
DOI：
10.1016/j.coastaleng.2013.10.010
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发表时间：
2014
影响因子：
4.4
通讯作者：
R. C. Ertekin
中科院分区：
文献类型：
--
作者：
B. B. Zhao;W. Y. Duan;R. C. Ertekin
最近衍生的（韦伯斯特等人，2011年），简化的高阶Green-Naghdi方程（GN-3，GN-5和GN-7）在这项工作中被用来模拟二维浅水波问题的转换。空间导数通过五点差分格式离散。提出了一种新的算法来求解所得到的块五对角矩阵。这些高层次的GN方程，然后利用开发一个数值波浪水槽。在水池的强迫边界处放置造波机，利用流函数理论产生非线性入射波。利用数值波浪水槽分析了大振幅波浪通过潜坝时的影响。在造波机附近（上波侧）设置阻尼区，以吸收来自水下拦门沙前侧的反射波。另一个阻尼区被放置在计算域的下波侧以吸收辐射波。在第一个测试案例中，杆的前斜率和后斜率都是温和的（Luth等人，1994年）。用GN-3、GN-5和GN-7方程模拟了波浪在沙洲上的传播。GN-3方程提供的时间历程与不同波浪仪的实验数据相比很好，除了在酒吧后面的。GN-5和GN-7方程的结果与这里考虑的所有实验数据进行了很好的比较。在第二个测试案例中，酒吧的前斜坡和后斜坡都很陡（Ohyama等人，1995年）。GN-5方程能很好地预测波浪高度。在第三个测试案例中，酒吧的前后斜坡交替，其中一个是温和的，另一个是陡峭的（Zou等人，2010年）。同样，GN-5方程的预测与实验数据吻合得很好。在本工作中考虑的所有测试情况中，在杆的波峰之后，GN-3和GN-5结果之间存在一些差异。GN-5方程和GN-7方程沿波浪水槽方向的数值结果沿着方向基本相同，但GN-7方程的计算时间较长。因此，GN-5结果在这里被接受为收敛的GN理论结果。数值验证表明，GN-5方程能较好地模拟淹没沙坝顶后的强非线性波和频散波。
Recently derived (Webster et al., 2011), simplified higher-level Green–Naghdi equations (GN-3, GN-5 and GN-7) are used in this work to simulate the transformation of two-dimensional, shallow-water wave problems. The spatial derivatives are discretized through a five-point difference scheme. A new algorithm is developed to solve the resulting block-pentadiagonal matrix. These high-level GN equations are then utilized to develop a numerical wave tank. A wave-maker is placed at the forcing boundary of the tank that uses the stream-function theory to generate nonlinear incident waves. The numerical wave tank is used to analyze the effects of large-amplitude waves passing over a submerged bar. A damping zone is placed near the wave-maker (up-wave side) to absorb the reflected waves from the front side of the submerged bar. Another damping zone is placed at the down-wave side of the computational domain to absorb the radiated waves. In the first test case, the front and back slopes of the bar are both mild (Luth et al., 1994). The waves that evolved over the bar are simulated by using the GN-3, GN-5 and GN-7 equations. The GN-3 equations provide time histories that compare well with the experimental data at different wave gauges, except at the ones behind the bar. The results of the GN-5 and GN-7 equations compare very well with all the experimental data considered here. In the second test case, the front and back slopes of the bar are both steep (Ohyama et al., 1995). The GN-5 equations predict the wave elevation well. In the third test case, the front and back slopes of the bar alternate, one of them being mild and the other one being steep (Zou et al., 2010). Again, the predictions of the GN-5 equations agree with the experimental data well. In all the test cases considered in this work, there are some differences between the GN-3 and GN-5 results after the crest of the bar. Numerical results obtained by the GN-5 and GN-7 equations are almost the same along the wave flume, but the GN-7 equations require more computational time. Therefore, the GN-5 results are accepted here as the converged GN theory results. The numerical validations show that the GN-5 equations can simulate the strongly nonlinear and dispersive waves observed behind the submerged bar crest satisfactorily.
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影响因子：
4.4
作者：
T. Ohyama;W. Kioka;A. Tada
通讯作者：
T. Ohyama;W. Kioka;A. Tada
影响因子：
4.4
作者：
M. Gobbi;J. Kirby
通讯作者：
M. Gobbi;J. Kirby
DOI：
10.1115/1.1537722
发表时间：
2003-02
影响因子：
1.6
作者：
J. W. Kim;K. Bai;R. Ertekin;W. Webster
通讯作者：
J. W. Kim;K. Bai;R. Ertekin;W. Webster
影响因子：
3.7
作者：
J. Shields;W. Webster
通讯作者：
J. Shields;W. Webster
DOI：
10.1098/rspa.2004.1305
发表时间：
2004-09-08
影响因子：
3.5
作者：
Lynett, P;Liu, PLF
通讯作者：
Liu, PLF