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Robust Detection of Singularities in Vector Fields Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Topological Features in Time-Dependent Advection-Diffusion Flow

Authors : Filip Sadlo, Grzegorz K. Karch, Thomas Ertl

Published in: Topological Methods in Data Analysis and Visualization III

Publisher: Springer International Publishing

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Abstract

Concepts from vector field topology have been successfully applied to a wide range of phenomena so far—typically to problems involving the transport of a quantity, such as in flow fields, or to problems concerning the instantaneous structure, such as in the case of electric fields. However, transport of quantities in time-dependent flows has so far been topologically analyzed in terms of advection only, restricting the approach to quantities that are solely governed by advection. Nevertheless, the majority of quantities transported in flows undergoes simultaneous diffusion, leading to advection-diffusion problems. By extending topology-based concepts with diffusion, we provide an approach for visualizing the mechanisms in advection-diffusion flow. This helps answering many typical questions in science and engineering that have so far not been amenable to adequate visualization. We exemplify the utility of our technique by applying it to simulation data of advection-diffusion problems from different fields.

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previous chapter Development of an Efficient and Flexible Pipeline for Lagrangian Coherent Structure Computation
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Literature
1.
D. Bürkle, T. Preußer, M. Rumpf, Transport and anisotropic diffusion in time-dependent flow visualization, in Proceedings of the IEEE Visualization, San Diego, 2001, pp. 61–67
2.
D. Eberly, Ridges in Image and Data Analysis. Computational Imaging and Vision (Kluwer, Boston, 1996)CrossRefMATH
3.
R. Fuchs, J. Kemmler, B. Schindler, F. Sadlo, H. Hauser, R. Peikert, Toward a Lagrangian vector field topology. Comput. Graph. Forum 29(3), 1163–1172 (2010)CrossRef
4.
C. Garth, G.-S. Li, X. Tricoche, C.D. Hansen, H. Hagen, Visualization of coherent structures in transient 2d flows, in Topology-Based Methods in Visualization II, ed. by H.-C. Hege, K. Polthier, G. Scheuermann (Springer, Berlin, 2009), pp. 1–13
5.
A. Globus, C. Levit, T. Lasinski, A tool for visualizing the topology of three-dimensional vector fields, in Proceedings of the IEEE Visualization, San Diego, 1991, pp. 33–40, 408
6.
7.
G. Haller, Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D 149(4), 248–277 (2001)CrossRefMATHMathSciNet
8.
9.
J. Helman, L. Hesselink, Representation and display of vector field topology in fluid flow data sets. IEEE Comput. 22(8), 27–36 (1989)CrossRef
10.
J. Helman, L. Hesselink, Visualizing vector field topology in fluid flows. IEEE Comput. Graph. Appl. 11(3), 36–46 (1991)CrossRef
11.
M. Hlawatsch, J. Vollrath, F. Sadlo, D. Weiskopf, Coherent structures of characteristic curves in symmetric second order tensor fields. IEEE Trans. Vis. Comput. Graph. 17(6), 781–794 (2011)CrossRef
12.
F. Hussain, Coherent structures and turbulence. J. Fluid Mech. 173, 303–356 (1986)CrossRef
13.
K. Ide, D. Small, S. Wiggins, Distinguished hyperbolic trajectories in time-dependent fluid flows: analytical and computational approach for velocity fields defined as data sets. Nonlinear Process. Geophys. 9(3/4), 237–263 (2002)CrossRef
14.
G.K. Karch, F. Sadlo, D. Weiskopf, C.-D. Munz, T. Ertl, Visualization of advection-diffusion in unsteady fluid flow. Comput. Graph. Forum 31(3), 1105–1114 (2012)CrossRef
15.
J. Kasten, I. Hotz, B. Noack, H.-C. Hege, On the extraction of long-living features in unsteady fluid flows, in Topological Methods in Data Analysis and Visualization. Theory, Algorithms, and Applications, ed. by V. Pascucci, X. Tricoche, H. Hagen, J. Tierny (Springer, Berlin/Heidelberg, 2010), pp. 115–126
16.
A. Kuhn, T. Senst, I. Keller, T. Sikora, H. Theisel, A Lagrangian framework for video analytics, in Proceedings of the IEEE Workshop on Multimedia Signal Processing, Banff, 2012
17.
Y. Levy, D. Degani, A. Seginer, Graphical visualization of vortical flows by means of helicity. AIAA 28(8), 1347–1352 (1990)CrossRef
18.
H. Löffelmann, H. Doleisch, E. Gröller, Visualizing dynamical systems near critical points, in Proceedings of the Spring Conference on Computer Graphics and Its Applications, Budmerice, 1998, pp. 175–184
19.
E.N. Lorenz, A study of the predictability if a 28-variable atmospheric model. Tellus 17, 321–333 (1965)CrossRef
20.
M. Otto, T. Germer, H. Theisel, Uncertain topology of 3d vector fields, in Proceedings of the IEEE Pacific Visualization Symposium, Hong Kong, 2011, pp. 67–74
21.
R. Peikert, M. Roth, The “parallel vectors” operator – a vector field visualization primitive, in Proceedings of the IEEE Visualization, San Francisco, 1999, pp. 263–270
22.
R. Peikert, F. Sadlo, Topology-guided visualization of constrained vector fields, in Topology-Based Methods in Visualization, ed. by H. Hauser, H. Hagen, H. Theisel (Springer, Berlin/New York, 2007), pp. 21–34CrossRef
23.
R. Peikert, F. Sadlo, Visualization methods for vortex rings and vortex breakdown bubbles, in Proceedings of the Joint Eurographics/IEEE VGTC Conference on Visualization, Norrköping, 2007, pp. 211–218
24.
R. Peikert, F. Sadlo, Flow topology beyond skeletons: visualization of features in recirculating flow, in Topology-Based Methods in Visualization II, ed. by H.-C. Hege, K. Polthier, G. Scheuermann (Springer, Berlin, 2009), pp. 145–160
25.
A.E. Perry, M.S. Chong, A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 19, 125–155 (1987)CrossRef
26.
A. Pobitzer, R. Peikert, R. Fuchs, B. Schindler, A. Kuhn, H. Theisel, K. Matković, H. Hauser, On the way towards topology-based visualization of unsteady flow – the state of the art, in Eurographics 2010 State of the Art Reports, Norrköping, 2010, pp. 137–154
27.
S.K. Robinson, Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639 (1991)CrossRef
28.
F. Sadlo, R. Peikert, Efficient visualization of Lagrangian coherent structures by filtered amr ridge extraction. IEEE Trans. Vis. Comput. Graph. 13(6), 1456–1463 (2007)CrossRef
29.
F. Sadlo, R. Peikert, Visualizing Lagrangian coherent structures and comparison to vector field topology, in Topology-Based Methods in Visualization II, ed. by H.-C. Hege, K. Polthier, G. Scheuermann (Springer, Berlin, 2009)
30.
F. Sadlo, M. Üffinger, T. Ertl, D. Weiskopf, On the finite-time scope for computing Lagrangian coherent structures from Lyapunov exponents, in Topological Methods in Data Analysis and Visualization II, ed. by R. Peikert et al. (Springer, Heidelberg/New York, 2012), pp. 269–281CrossRef
31.
F. Sadlo, D. Weiskopf, Time-dependent 2-d vector field topology: an approach inspired by Lagrangian coherent structures. Comput. Graph. Forum 29(1), 88–100 (2010)CrossRef
32.
A. Sanderson, G. Chen, X. Tricoche, D. Pugmire, S. Kruger, J. Breslau, Analysis of recurrent patterns in toroidal magnetic fields. IEEE Trans. Vis. Comput. Graph. 16(6), 1431–1440 (2010)CrossRef
33.
A. Sanderson, C.R. Johnson, R.M. Kirby, Display of vector fields using a reaction-diffusion model, in Proceedings of the IEEE Visualization, Austin, 2004, pp. 115–122
34.
B. Schindler, R. Fuchs, S. Barp, J. Waser, A. Pobitzer, R. Carnecky, K. Matkovic, R. Peikert, Lagrangian coherent structures for design analysis of revolving doors. IEEE Trans. Vis. Comput. Graph. 18(12), 2159–2168 (2012)CrossRef
35.
D. Schneider, J. Fuhrmann, W. Reich, G. Scheuermann, A variance based ftle-like method for unsteady uncertain vector fields, in Topological Methods in Data Analysis and Visualization II, ed. by R. Peikert et al. (Springer, Heidelberg/New York, 2012), pp. 255–268CrossRef
36.
S.C. Shadden, F. Lekien, J.E. Marsden, Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Phys. D: Nonlinear Phenom. 212, 271–304 (2005)CrossRefMATHMathSciNet
37.
K. Shi, H. Theisel, H. Hauser, T. Weinkauf, K. Matkovic, H.-C. Hege, H.-P. Seidel, Path line attributes – an information visualization approach to analyzing the dynamic behavior of 3D time-dependent flow fields, in Topology-Based Methods in Visualization II, ed. by H.-C. Hege, K. Polthier, G. Scheuermann (Springer, Berlin, 2009), pp. 75–88CrossRef
38.
D. Sujudi, R. Haimes, Identification of swirling flow in 3d vector fields, in Proceedings of the 12th AIAA Computational Fluid Dynamics Conference, 1995, pp. 95–1715
39.
H. Theisel, J. Sahner, T. Weinkauf, H.-C. Hege, H.-P. Seidel, Extraction of parallel vector surfaces in 3D time-dependent fields and application to vortex core line tracking, in Proceedings of the IEEE Visualization, Minneapolis, 2005, pp. 631–638
40.
H. Theisel, T. Weinkauf, H.-C. Hege, H.-P. Seidel, Saddle connectors – an approach to visualizing the topological skeleton of complex 3d vector fields, in Proceedings of the IEEE Visualization, Seattle, 2003, pp. 225–232
41.
H. Theisel, T. Weinkauf, H.-C. Hege, H.-P. Seidel, Stream line and path line oriented topology for 2d time-dependent vector fields, in Proceedings of the IEEE Visualization, Austin, 2004, pp. 321–328
42.
X. Tricoche, C. Garth, A. Sanderson, K. Joy, Visualizing invariant manifolds in area-preserving maps, in Topological Methods in Data Analysis and Visualization II, ed. by R. Peikert et al. (Springer, Heidelberg/New York, 2012), pp. 109–124
43.
X. Tricoche, M. Hlawitschka, S. Barakat, C. Garth, Beyond topology: a Lagrangian metaphor to visualize the structure of 3d tensor fields, in New Developments in the Visualization and Processing of Tensor Fields, ed. by D. Laidlaw, A. Vilanova (Springer, Berlin/New York, 2012)
44.
M. Üffinger, F. Sadlo, T. Ertl, A time-dependent vector field topology based on streak surfaces. IEEE Trans. Vis. Comput. Graph. 19(3), 379–392 (2013)CrossRef
45.
T. Weinkauf, H. Theisel, H.-C. Hege, H.-P. Seidel, Boundary switch connectors for topological visualization of complex 3D vector fields, in Proceedings of the VisSym, Konstanz, 2004, pp. 183–192
Metadata
Title
Topological Features in Time-Dependent Advection-Diffusion Flow
Authors
Filip Sadlo
Grzegorz K. Karch
Thomas Ertl
Copyright Year
2014
Book
Topological Methods in Data Analysis and Visualization III

Print ISBN: 978-3-319-04098-1

Electronic ISBN: 978-3-319-04099-8

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-04099-8_14

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