A comparison of blob methods for vortex sheet roll-up
A comparison of blob methods for vortex sheet roll-up
复制标题
涡流片卷起的斑点方法的比较
DOI：
--
复制
发表时间：
2006
影响因子：
3.7
通讯作者：
Lan D. Pham
中科院分区：
文献类型：
--
作者：
G. Baker;Lan D. Pham
旋涡片的运动容易受到开尔文-亥姆霍兹不稳定性的影响。现在有大量的证据表明，不稳定性导致在有限时间内曲率奇点的形成。涡旋团方法为涡旋片的运动提供了一种正则化方法。涡团法生成的曲线不是在有限时间内形成曲率奇点，而是形成螺旋形。理论表明，随着斑点大小的消失，这些螺旋将收敛到欧拉方程的经典弱解。该理论假定blob方法是薄片速度与适当选择的平滑函数卷积的结果。我们考虑了四种不同的blob方法，两种是由适当选择平滑函数产生的，另两种不是。数值结果表明，这些方法生成的曲线形成不同的螺旋，但随着斑点大小的消失，它们都接近相同的弱极限。通过适当地缩放距离和时间与团块大小，由不同团块大小产生的螺旋族几乎完美地坍缩成一个螺旋。这一观察是发展渐近理论以详细描述弱解性质的下一步。
The motion of vortex sheets is susceptible to the onset of the Kelvin–Helmholz instability. There is now a large body of evidence that the instability leads to the formation of a curvature singularity in finite time. Vortex blob methods provide a regularization for the motion of vortex sheets. Instead of forming a curvature singularity in finite time, the curves generated by vortex blob methods form spirals. Theory states that these spirals will converge to a classical weak solution of the Euler equations as the blob size vanishes. This theory assumes that the blob method is the result of a convolution of the sheet velocity with an appropriate choice of a smoothing function. We consider four different blob methods, two resulting from appropriate choices of smoothing functions and two not. Numerical results indicate that the curves generated by these methods form different spirals, but all approach the same weak limit as the blob size vanishes. By scaling distances and time appropriately with blob size, the family of spirals generated by different blob sizes collapse almost perfectly to a single spiral. This observation is the next step in developing an asymptotic theory to describe the nature of the weak solution in detail.