Journal of Visualization

, Volume 19, Issue 1, pp 115–128 | Cite as

Visualization of 2D unsteady flow using streamline-based concepts in space-time

  • Grzegorz K. Karch
  • Filip Sadlo
  • Daniel Weiskopf
  • Thomas Ertl
Regular Paper


Treating time as the third dimension of 2D time-dependent flow enables the application of a wide variety of visualization techniques for 3D stationary vector fields. In the resulting space-time representation, 3D streamlines represent 2D pathlines of the original field. In this paper, we investigate the application of different streamline-based visualization concepts to the 3D space-time representation of 2D time-dependent flow. As a consequence, we obtain from each streamline-based concept a Galilean-invariant counterpart that takes the time dependence of the original field explicitly into account. We show the advantages of the overall approach for vortex analysis and the analysis of the dynamics of material lines. In particular, we employ the concept for the extraction of vortex centers, vortex core regions, and the visualization of material line dynamics using streamsurface integration and line integral convolution in the space-time field. We exemplify the utility of our visualization approach using two 2D time-dependent datasets that exhibit vortical flow.

Graphical Abstract


Space-time visualization Galilean invariance Computational visualization 

Mathematics Subject Classification




The authors would like to thank the Deutsche Forschungsgemeinschaft (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology (EXC 310/1) and the Collaborative Research Centre SFB-TRR 75 at the University of Stuttgart.


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Copyright information

© The Visualization Society of Japan 2015

Authors and Affiliations

  • Grzegorz K. Karch
    • 1
  • Filip Sadlo
    • 1
  • Daniel Weiskopf
    • 1
  • Thomas Ertl
    • 1
  1. 1.University of StuttgartStuttgartGermany

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