Topological Methods for Visualizing Vortical Flows

The paper describes the application of topological methods to the visualization of vortical flow patterns that arise in simulations from Computational Fluid Dynamics. Two techniques are presented: the first is concerned with the exploration of complicated, instanta- neous flow structures while the second one permits the visualization of their temporal evolu- tion in large-scale transient simulations. In both cases the mathematical framework is derived from the notion of parametric topology. This yields a unified formalism that permits to effi- ciently address the challenges raised by typical flow problems. The benefits of this approach are demonstrated in the analysis and visualization of transient vortical flows that undergo the phenomenon of vortex breakdown.

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

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

[3]  A. Andronov,et al.  Qualitative Theory of Second-order Dynamic Systems , 1973 .

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

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

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

[7]  Ronald Peikert,et al.  The "Parallel Vectors" operator-a vector field visualization primitive , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

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

[9]  William E. Lorensen,et al.  The stream polygon-a technique for 3D vector field visualization , 1991, Proceeding Visualization '91.

[10]  D. Sujudi,et al.  Identification of Swirling Flow in 3-D Vector Fields , 1995 .

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

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

[13]  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..

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

[15]  Robert Haimes,et al.  Vortex identification—applications in aerodynamics: a case study , 1997 .

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

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

[18]  Xavier Tricoche,et al.  Tracking of vector field singularities in unstructured 3D time-dependent datasets , 2004, IEEE Visualization 2004.

[19]  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..