An objective-adaptive refinement criterion based on modified ridge extraction method for finite-time Lyapunov exponent (FTLE) calculation

  • Haotian Hang
  • Bin Yu
  • Yang Xiang
  • Bin ZhangEmail author
  • Hong Liu
Regular Paper


Visualizing finite-time Lyapunov exponent (FTLE) efficiently and accurately has long been a research objective in identifying the coherent structures of turbulence or vortex flows. In this field, adaptive mesh refinement shows its effectiveness. The proposed objective-adaptive refinement (OAR) criterion can refine adaptive particles in the vicinity of FTLE ridges by a modified gradient climbing method. While error-based refinement methods suffer from ineffective refinement when the initial velocity field contains error, and refinement methods based on FTLE magnitude have issues with undulate ridges, our objective OAR criterion always steers the refinement toward the vicinity of FTLE ridges. Testing cases include Bickley jet, mild FTLE ridge and experimental single vortex, three-dimensional ABC flow. The results demonstrate that the proposed OAR criterion can give the right refinement region, and thus enhance computation efficiency, by means of accurate extraction of FTLE ridges.

Graphic abstract


Flow structures visualization Objective-adaptive refinement (OAR) Lagrangian coherent structures (LCS) Finite-time Lyapunov exponent (FTLE) 



The authors would like to thank the Center for High-Performance Computing of SJTU for providing the super computer \(\pi \) to support this research. This work is supported by the National Natural Science Foundation of China (NSFC-91741113) and National Science Foundation for Young Scientists of China (Grant No. 51676203). Furthermore, Geng Liang is appreciated in assistance in three-dimensional cases and refinement criterion. Also, Chunhui Tang, Haiyan Lin and Linying Li are appreciated in assisting the completion of the paper.


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Copyright information

© The Visualization Society of Japan 2019

Authors and Affiliations

  • Haotian Hang
    • 1
  • Bin Yu
    • 1
  • Yang Xiang
    • 1
  • Bin Zhang
    • 1
    Email author
  • Hong Liu
    • 1
  1. 1.School of Aeronautics and AstronauticsShanghai Jiao Tong UniversityShanghaiChina

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