Vortex methods. I. Convergence in three dimensions
Vortex methods. I. Convergence in three dimensions
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DOI：
10.1090/s0025-5718-1982-0658212-5
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发表时间：
1982-09
影响因子：
2
通讯作者：
By J. Thomas Beale;A. Majda
中科院分区：
文献类型：
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作者：
By J. Thomas Beale;A. Majda
近年来，用涡方法模拟三维不可压缩流体流动已发展出几种不同的方法。一些版本使用详细的跟踪涡丝结构和这些丝的局部曲率，而其他方法只需要粗略的信息，如二维情况下的涡滴。这种“粗糙”的算法能准确地解释涡旋的拉伸和收敛吗？我们通过构建一类新的“粗糙”三维涡旋方法来肯定地回答这个问题，然后证明这些方法是稳定和收敛的，甚至可以具有任意高阶精度，而不会比其他“粗糙”版本更昂贵涡旋算法。
Recently several different approaches have been developed for the simulation of three-dimensional incompressible fluid flows using vortex methods. Some versions use detailed tracking of vortex filament structures and often local curvatures of these filaments, while other methods require only crude information, such as the vortex blobs of the two-dimensional case. Can such "crude" algorithms accurately account for vortex stretching and converge? We answer this question affirmatively by constructing a new class of "crude" three-dimensional vortex methods and then proving that these methods are stable and convergent, and can even have arbitrarily high order accuracy without being more expensive than other "crude" versions of the vortex algorithm.