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Filtering of FTLE for Visualizing Spatial Separation in Unsteady 3D Flow

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Topological Methods in Data Analysis and Visualization II

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

In many cases, feature detection for flow visualization is structured in two phases: first candidate identification, and then filtering. With this paper, we propose to use the directional information contained in the finite-time Lyapunov exponents (FTLE) computation, in order to filter the FTLE field. In this way we focus on those separation structures that delineate flow compartments which develop into different spatial locations, as compared to those that separate parallel flows of different speed. We provide a discussion of the underlying theory and our related considerations. We derive a new filtering scheme and demonstrate its effect in the context of several selected fluid flow cases, especially in comparison with unfiltered FTLE visualization. Since previous work has provided insight with respect to the studied flow patterns, we are able to provide a discussion of the resulting visible separation structures.

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Author information

Authors and Affiliations

  1. Department of informatics, University of Bergen, 7803, 5020, Bergen, Norway

    Armin Pobitzer & Helwig Hauser

  2. Scientific Visualization Group, ETH Zurich, Rämistrasse 101, 8092, Zurich, Switzerland

    Ronald Peikert & Raphael Fuchs

  3. Department of Simutation and Graphics, University of Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Holger Theisel

Authors
  1. Armin Pobitzer
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  2. Ronald Peikert
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  3. Raphael Fuchs
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  4. Holger Theisel
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  5. Helwig Hauser
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Corresponding author

Correspondence to Armin Pobitzer .

Editor information

Editors and Affiliations

  1. Inst. Computational Science, CAB G 65.1, ETH Zürich, Universitätsstraße 6, Zürich, 8092, Switzerland

    Ronald Peikert

  2. , Dept. of Informatics, University of Bergen, Bergen, Norway

    Helwig Hauser

  3. , School of Computing, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, United Kingdom

    Hamish Carr

  4. , Computational Science, ETH Zürich, Universitätsstraße 6, Zürich, 8092, Switzerland

    Raphael Fuchs

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Pobitzer, A., Peikert, R., Fuchs, R., Theisel, H., Hauser, H. (2012). Filtering of FTLE for Visualizing Spatial Separation in Unsteady 3D Flow. In: Peikert, R., Hauser, H., Carr, H., Fuchs, R. (eds) Topological Methods in Data Analysis and Visualization II. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23175-9_16

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