University of Bergen | Faculty of Mathematics and Natural Sciences | Department of Informatics | Visualization Group
Visualization
You are here: Department of Informatics > Visualization Group > Publications > fuchs10lagrangian
 Visualization
 > about
 > team & contact info
 > research
 > publications
 > projects
 > teaching
 > seminars
 > resources
 > network
 > events
 > links

Toward a Lagrangian Vector Field Topology

Raphael Fuchs, Jan Kemmler, Benjamin Schindler, Jürgen Waser, Filip Sadlo, Helwig Hauser, Ronald Peikert

ARTICLE, Computer Graphics Forum, june, 2010

Abstract

In this paper we present an extended critical point concept which allows us to apply vector field topology in the case of unsteady flow. We propose a measure for unsteadiness which describes the rate of change of the velocities in a fluid element over time. This measure allows us to select particles for which topological properties remain intact inside a finite spatio-temporal neighborhood. One benefit of this approach is that the classification of critical points based on the eigenvalues of the Jacobian remains meaningful. In the steady case the proposed criterion reduces to the classical definition of critical points. As a first step we show that finding an optimal Galilean frame of reference can be obtained implicitly by analyzing the acceleration field. In a second step we show that this can be extended by switching to the Lagrangian frame of reference. This way the criterion can detect critical points moving along intricate trajectories. We analyze the behavior of the proposed criterion based on two analytical vector fields for which a correct solution is defined by their inherent symmetries and present results for numerical vector fields.

Published

Computer Graphics Forum

Media

  • www
  • Click to view
  • Click to view

BibTeX

@article{fuchs10lagrangian,
  author = {Raphael Fuchs and Jan Kemmler and Benjamin Schindler and Jürgen Waser and 
  Filip Sadlo and Helwig Hauser and Ronald Peikert},
  title = {Toward a Lagrangian Vector Field Topology},
  year = {2010},
  month = {june},
  abstract = {In this paper we present an extended critical point concept which 
allows us to apply vector field topology in the case of unsteady flow. We propose 
a measure for unsteadiness which describes the rate of change of the velocities in
a fluid element over time. This measure allows us to select particles for which 
topological properties remain intact inside a finite spatio-temporal neighborhood. 
One benefit of this approach is that the classification of critical points based 
on the eigenvalues of the Jacobian remains meaningful. In the steady case the 
proposed criterion reduces to the classical definition of critical points. As a 
first step we show that finding an optimal Galilean frame of reference can be 
obtained implicitly by analyzing the acceleration field. In a second step we show 
that this can be extended by switching to the Lagrangian frame of reference. This 
way the criterion can detect critical points moving along intricate trajectories. 
We analyze the behavior of the proposed criterion based on two analytical vector 
fields for which a correct solution is defined by their inherent symmetries and 

  journal = {Computer Graphics Forum},
  event = "EuroVis 2010",
  volume = {29},
  number = {3},
  pages = {1163--1172},
  location = "Bordeaux, France",


  URL = {http://dx.doi.org/10.1111/j.1467-8659.2009.01686.x},

}






 Last Modified: Jean-Paul Balabanian, 2014-04-09