Fast Computation of FTLE Fields for Unsteady Flows : A Comparison of Methods
Fast Computation of FTLE Fields for Unsteady Flows : A Comparison of Methods
复制标题
非定常流 FTLE 场的快速计算：方法比较
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
C. Rowley
中科院分区：
文献类型：
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作者：
S. Brunton;C. Rowley
本文提出了新的，有效的方法计算有限时间李雅普诺夫指数（FTLE）领域的非定常流动。该方法近似的粒子流图，以消除冗余的粒子积分在相邻的流图计算。基于中间流图的合成研究了两类流图近似;单向近似通过合成一些较小的时间-h图来构造时间-T图，而双向近似通过合成正时间和负时间图来构造流图。单向方法被证明是快速和准确的，虽然它是内存密集型的。双向方法也是快速的，并且使用显著更少的存储器;然而，它容易产生与相反时间的拉格朗日相干结构对准的大误差。该算法的实现和比较三个例子的流体流动：双涡旋，低雷诺数俯仰平板，和非定常ABC流。
This paper presents new, efficient methods for computing finite-time Lyapunov exponent (FTLE) fields in unsteady flows. The methods approximate the particle flow map to eliminate redundant particle integrations in neighboring flow map calculations. Two classes of flow map approximations are investigated based on composition of intermediate flow maps; unidirectional approximation constructs a time-T map by composing a number of smaller time-h maps, while bidirectional approximation constructs a flow map by composing both positive and negative-time maps. The unidirectional method is shown to be fast and accurate, although it is memory intensive. The bidirectional method is also fast and uses significantly less memory; however, it is prone to large error which is aligned with the opposite-time Lagrangian coherent structures. The algorithms are implemented and compared on three example fluid flows: the double gyre, a low Reynolds number pitching flat plate, and unsteady ABC flow.