Simple and efficient numerical methods for vortex sheet motion with surface tension
Simple and efficient numerical methods for vortex sheet motion with surface tension
复制标题
具有表面张力的涡流片运动的简单有效的数值方法
DOI：
10.1002/fld.3857
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发表时间：
2014
影响因子：
1.8
通讯作者：
Woonjae Hwang
中科院分区：
文献类型：
--
作者：
Suyeon Shin;Sung;Woonjae Hwang
我们给出了两种简单有效的计算表面张力涡片的显式方法。第一种是标准点涡法，由于高模波动的虚假增长，这种方法在有表面张力的情况下是不稳定的。首次证明了标准点涡法能够通过傅立叶滤波来计算有表面张力的涡片运动。第二种方法是对Pullin方法的改进，使用中心差分进行数值微分。该方法比其他谱方法更易于实现，且不存在混叠不稳定性。我们给出了数值方法的线性稳定性分析，并给出了涡片的长时间演化结果。我们还提出了一种新的控制点聚类的重分布过程，通过设置邻近点之间的最小和最大距离限制。对于显式方法的长时间计算，该方法是非常有效的。版权所有©2013 John Wiley&Sons，Ltd.
We present two simple and efficient explicit methods for the vortex sheet with surface tension. The first one is the standard point vortex method, which has been known to be unstable in the presence of surface tension, due to spurious growth of waves of high modes. We show, for the first time, that the standard point vortex method is able to calculate the vortex sheet motion with surface tension by employing a Fourier filtering. The second method is a modification of the Pullin method using central differences for numerical differentiations. This method is more convenient to implement than other spectral methods and is free from the aliasing instability. We give a linear stability analysis for the numerical methods and show results for the long‐time evolution of the vortex sheet. We also propose a new redistribution procedure to control point clustering, by setting limits of minimum and maximum distances between neighboring points. This procedure is found to be very efficient for long‐time computations of the explicit methods. Copyright © 2013 John Wiley & Sons, Ltd.