A fast method for nonlinear three-dimensional free-surface waves
A fast method for nonlinear three-dimensional free-surface waves
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DOI：
10.1098/rspa.2006.1706
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发表时间：
2006-09-08
影响因子：
3.5
通讯作者：
Dias, Frederic
中科院分区：
文献类型：
--
作者：
Fochesato, Christophe;Dias, Frederic
提出了一种求解完全非线性有自由面势流方程的有效数值模型。类似于由Grilli等人开发的代码（Grilli等人，2001 Int. J. Numer.方法流体35，829-867），它使用高阶三维边界元法结合混合欧拉-拉格朗日时间更新，基于二阶显式泰勒展开与自适应时间步长。这些方法被认为是准确的，但昂贵。通过引入快速多极子算法，大大提高了程序的效率。该算法通过替换迭代求解器中的每个矩阵向量积，避免了影响矩阵的建立，将计算复杂度从O（N-2）降低到接近O（N），其中N为边界上的节点数。通过三维斜底上孤立波倾覆的算例说明了该方法的有效性。对于这个测试用例，加速方法确实比前一种方法快得多，即使对于非常粗糙的网格也是如此。例如，对于相同的全局精度，对于N=6022，获得了复杂度的因子6的减少。加速的代码允许更复杂的物理问题的研究和几个例子。
An efficient numerical model for solving fully nonlinear potential flow equations with a free surface is presented. Like the code that was developed by Grilli et al. (Grilli et al. 2001 Int. J. Numer. Methods Fluids 35, 829-867), it uses a high-order three-dimensional boundary-element method combined with mixed Eulerian-Lagrangian time updating, based on second-order explicit Taylor expansions with adaptive time-steps. Such methods are known to be accurate but expensive. The efficiency of the code has been greatly improved by introducing the fast multipole algorithm. By replacing every matrix-vector product of the iterative solver and avoiding the building of the influence matrix, this algorithm reduces the computing complexity from O(N-2) to nearly O(N), where N is the number of nodes on the boundary. The performance of the method is illustrated by the example of the overturning of a solitary wave over a three-dimensional sloping bottom. For this test case, the accelerated method is indeed much faster than the former one, even for quite coarse grids. For instance, a reduction of the complexity by a factor six is obtained for N=6022, for the same global accuracy. The acceleration of the code allows the study of more complex physical problems and several examples are presented.