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
AbstractIn 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
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},
}
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