The nonlinear evolution of vortex sheets with surface tension in axisymmetric flows
The nonlinear evolution of vortex sheets with surface tension in axisymmetric flows
复制标题
轴对称流中表面张力涡片的非线性演化
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
Q. Nie
中科院分区：
文献类型：
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作者：
Q. Nie
摘要界面流中表面张力的存在，通常会对显式时间积分方法的稳定性产生严重的限制。此外，高阶项的非局部性和非线性给隐式方法的应用带来了困难。本文提出了一种用边界积分方法计算轴对称流中有表面张力的流体界面运动的计算方法。该方法是基于自适应求积的主值积分和小规模分解的表面张力的治疗，通过一个矢量势制定。在轴对称流动中涡面演化与表面张力的背景下进行的方法的研究。该方法被认为是准确的，有效的，和强大的。数值模拟表明，具有表面张力的涡面动力学经常导致拓扑奇异性（即，自相交）。远离对称轴，这些奇点与二维流动中发现的奇点相似。在对称轴附近出现的奇异点有不同的形式。
Abstract The presence of surface tension for interfacial flows usually leads to severe stability constraints for explicit time integration methods. Moreover, the nonlocality and nonlinearity of the high-order terms make the application of implicit methods difficult. In this paper, a computational strategy is presented for computing the motion of fluid interfaces with surface tension in axisymmetric flows using boundary integral techniques. This method is based on adaptive quadratures for the principal-value integrals and a small-scale decomposition for the treatment of surface tension through a vector-potential formulation. A study of the method is conducted in the context of vortex sheet evolution with surface tension in axisymmetric flows. The method is found to be accurate, efficient, and robust. Numerical simulations indicate that the dynamics of vortex sheets with surface tension frequently result in topological singularities (i.e., self-intersection). Away from the axis of symmetry, these singularities are similar to those found in the two-dimensional flows. Singularities occurring near the axis of symmetry take a different form.