Tracking of vector field singularities in unstructured 3D time-dependent datasets

We present an approach for monitoring the positions of vector field singularities and related structural changes in time-dependent datasets. The concept of singularity index is discussed and extended from the well-understood planar case to the more intricate three-dimensional setting. Assuming a tetrahedral grid with linear interpolation in space and time, vector field singularities obey rules imposed by fundamental invariants (Poincare index), which we use as a basis for an efficient tracking algorithm. We apply the presented algorithm to CFD datasets to illustrate its purpose. We examine structures that exhibit topological variations with time and describe some of the insight gained with our method. Examples are given that show a correlation in the evolution of physical quantities that play a role in vortex breakdown.

[1]  D. Hestenes,et al.  Clifford Algebra to Geometric Calculus , 1984 .

[2]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[3]  Bernd Hamann,et al.  Topological segmentation in three-dimensional vector fields , 2004, IEEE Transactions on Visualization and Computer Graphics.

[4]  Al Globus,et al.  A tool for visualizing the topology of three-dimensional vector fields , 1991, Proceeding Visualization '91.

[5]  Xin Wang,et al.  Tracking and Visualizing Turbulent 3D Features , 1997, IEEE Trans. Vis. Comput. Graph..

[6]  Stephen Mann,et al.  Computing singularities of 3D vector fields with geometric algebra , 2002, IEEE Visualization, 2002. VIS 2002..

[7]  Deborah Silver,et al.  Visualizing features and tracking their evolution , 1994, Computer.

[8]  David C. Banks,et al.  Extracting iso-valued features in 4-dimensional scalar fields , 1998, VVS '98.

[9]  Simon Tavener,et al.  On the creation of stagnation points near straight and sloped walls , 2000 .

[10]  Jian Chen,et al.  The feature tree: visualizing feature tracking in distributed AMR datasets , 2003, IEEE Symposium on Parallel and Large-Data Visualization and Graphics, 2003. PVG 2003..

[11]  Hans-Peter Seidel,et al.  Feature Flow Fields , 2003, VisSym.

[12]  Hans Hagen,et al.  Topology tracking for the visualization of time-dependent two-dimensional flows , 2002, Comput. Graph..

[13]  Ronald Peikert,et al.  Vortex Tracking in Scale-Space , 2002, VisSym.

[14]  Lambertus Hesselink,et al.  Visualizing vector field topology in fluid flows , 1991, IEEE Computer Graphics and Applications.

[15]  Xavier Tricoche,et al.  Surface techniques for vortex visualization , 2004, VISSYM'04.

[16]  Hans-Peter Seidel,et al.  Saddle connectors - an approach to visualizing the topological skeleton of complex 3D vector fields , 2003, IEEE Visualization, 2003. VIS 2003..

[17]  David C. Banks,et al.  Extracting iso-valued features in 4-dimensional scalar fields , 1998, IEEE Symposium on Volume Visualization (Cat. No.989EX300).

[18]  Robert Haimes,et al.  Vortex identification-applications in aerodynamics: a case study , 1997, Proceedings. Visualization '97 (Cat. No. 97CB36155).