Lagrangian coherent structures with guaranteed material separation

Authors:
T. Germer;M. Otto;R. Peikert;H. Theisel
Affiliations:
University of Magdeburg, Germany;University of Magdeburg, Germany;ETH Zurich, Switzerland;University of Magdeburg, Germany
Venue:
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
Year:
2011

Citing 12
Cited 0

Ridges for image analysis

Journal of Mathematical Imaging and Vision
Edge Detection and Ridge Detection with Automatic Scale Selection

International Journal of Computer Vision
Lagrangian coherent structures and mixing in two-dimensional turbulence

Physica D
Distinguished material surfaces and coherent structures in three-dimensional fluid flows

Physica D
Ridge-valley lines on meshes via implicit surface fitting

ACM SIGGRAPH 2004 Papers
Topological Methods for 2D Time-Dependent Vector Fields Based on Stream Lines and Path Lines

IEEE Transactions on Visualization and Computer Graphics
Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction

IEEE Transactions on Visualization and Computer Graphics
Efficient Computation and Visualization of Coherent Structures in Fluid Flow Applications

IEEE Transactions on Visualization and Computer Graphics
Efficient Morse Decompositions of Vector Fields

IEEE Transactions on Visualization and Computer Graphics
Pathline predicates and unsteady flow structures

The Visual Computer: International Journal of Computer Graphics
Crease Surfaces: From Theory to Extraction and Application to Diffusion Tensor MRI

IEEE Transactions on Visualization and Computer Graphics
Vortex and Strain Skeletons in Eulerian and Lagrangian Frames

IEEE Transactions on Visualization and Computer Graphics

Quantified Score

Hi-index	0.00

Visualization

Abstract

Given an unsteady flow field, one common way to compute Lagrangian Coherent Structures (LCS) is to extract extremal structures of the Finite Time Lyapunov Exponent (FTLE). Experience has shown that the resulting structures are often close to material structures (i.e., material lines or material surfaces). Moreover, it has been proven that for an integration time converging to infinity, they converge to exact material structures. However, due to the finite integration time in FTLE, they are generally not exact material structures. In this paper we introduce a modification of the FTLE method which is guaranteed to produce separating material structures as features of a scalar field. We achieve this by incorporating the complete available integration time both in forward and backward direction, and by choosing an appropriate definition for separating structures. We apply our method to two test data sets and show the differences to classical FTLE.