Traveling Water Waves
Traveling Water Waves
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行进的水波
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
D. Nicholls
中科院分区：
文献类型：
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作者：
D. Nicholls
我们提出了一个数值延拓方法的行波解的全水波问题使用谱配置离散。水波问题根据引起扎哈罗夫？克雷格？Sulem公式，并通过引入相速度矢量作为参数，研究了行波.我们通过数值延拓方法跟踪从平凡解分支分叉出来的非平凡解分支。诸如投影和过滤之类的技术允许计算在分支上进行更大的距离，并且并行性允许计算更大的问题。我们得出结论，包括形成的三维问题的六边形图案的结果。
We present a numerical continuation method for traveling wave solutions to the full water wave problem using a spectral collocation discretization. The water wave problem is reformulated in terms of surface variables giving rise to the Zakharov?Craig?Sulem formulation, and traveling waves are studied by introducing a phase velocity vector as a parameter. We follow non-trivial solution branches bifurcating from the trivial solution branch via numerical continuation methods. Techniques such as projections and filtering allow the computation to proceed for greater distances up the branch, and parallelism allows the computation of larger problems. We conclude with results including the formation of hexagonal patterns for the three dimensional problem.