.png){kind=icon}
返回
EULERIAN METHODS FOR VISUALIZING CONTINUOUS DYNAMICAL SYSTEMS USING LYAPUNOV EXPONENTS
.png){kind=icon}
OA
AI
DOI：10.1137/16M1066890.png)
.png){kind=icon}
.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
We propose a new Eulerian numerical approach for constructing forward flow maps in continuous dynamical systems. The new algorithm improves the original formulation developed in [S. Leung, T. Comput. Phys., 230 (2011), pp. 3500-3524; S. Leung, Chaos, 23 (2013), 043132] so that the associated PDEs are solved forward in time and, therefore, the forward flow map can now be determined on the fly. Thanks to the simplicity of the implementations, we are now able to efficiently compute the unstable coherent structures in the flow based on quantities like the finite time Lyapunov exponent (FTLE), the finite size Lyapunov exponent (FSLE) and also a related infinitesimal size Lyapunov exponent (ISLE). When applied to the ISLE computations, the Eulerian method is particularly computationally efficient. For each separation factor r in the definition of the ISLE, typical Lagrangian methods are required to shoot and monitor an individual set of ray trajectories. If the scale factor in the definition changes, these methods have to begin the computations all over again. The proposed Eulerian method, however, needs to extract only an isosurface of volumetric data for an individual value of r, which can be easily done using any well-developed efficient interpolation method or simply an isosurface extraction algorithm. Moreover, we provide a theoretical link between the FTLE and ISLE fields, which explains the similarity in these solutions observed in various applications.
Keyword:
Eulerian methods
dynamical systems
Lyapunov exponents
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
2.6
论文数:
5.1K
被引数:
1.8W
机构
引用论文
Development and Validation of the University of Washington Clinical Assessment of Music Perception Test华盛顿大学音乐知觉临床评估测试的开发和验证OAAI
OAAI分享收藏
分享收藏Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence.png)
PHYSICS OF FLUIDS
PHYSICS OF FLUIDSIF4.3
PREAI
分享收藏
查看更多内容