Please note: this page is currently under construction.

Presentation Slides

Part I: Theoretical Background and Integration-Based Methods
Part II: Lagrangian Techniques
Part III: Large Data and Parallel Visualization
Part IV: Flow Visualization Applications in Biomedicine
Part V: Vector Field Visualization in Aeronautics Research

Software

The VisIt Visualization Toolkit – parallel interactive visualization software for very large time-varying vector fields.
https://wci.llnl.gov/codes/visit/

References & Further Reading

Theoretical Background and Integration-Based Methods

D. Bauer and R. Peikert. A case study in selective visualization of unsteady 3d flow. In IEEE Computer Society Press, editor, IEEE Visualization Proceedings, pages 525–528, Los Alamitos, CA, 2002.
D. Banks and B. Singer. A Predictor-Corrector Technique for Visualizing Unsteady Flow. IEEE Transactions on Visualization and Computer Graphics, 1(2):151–163, 1995.
J. R. Cash and A. H. Karp. A variable order runge-kutta method for initial value problems with rapidly varying right-hand sides. ACM Trans. Math. Softw., 16:201–222, 1990.
A. J. Chorin and J. E. Marsden. A Mathematical Introduction to Fluid Mechanics. Texts in Applied Mathematics. Springer, Berlin, 2004.
U. Dallmann. Topological Structures of Three-Dimensional Flow Separations. Technical Report 221-82 A 07, Deutsche Forschungs- und Versuchsanstalt fuer Luft- und Raumfahrt, 1983.
C. Garth, R.S. Laramee, X. Tricoche, J. Schneider, and H. Hagen. Extraction and visualization of swirl and tumble motion from engine simulation data. In Proceedings of The Topology-Based Methods in Visualization Workshop, 2006.
I. Gladwell, L. F. Shampine, L. S. Baca, and R. W. Brankin. Practical aspects of interpolation in runge-kutta codes. SIAM J. Sci. Stat. Comput., 8(3):322–341, 1987.
C. Garth, X. Tricoche, and G. Scheuermann. Tracking of vector field singularities in unstructured 3D time-dependent data sets. In Proceedings of IEEE Visualization 2004, pages 329–226, 2004.
C. Garth, X. Tricoche, T. Salzbrunn, and G. Scheuermann. Surface techniques for vortex visualization. In Proceedings Eurographics - IEEE TCVG Symposium on Visualization, May 2004.
C. Garth, X. Tricoche, A. Wiebel, and K. I. Joy. On the role of domain-specific knowledge in the visualization of technical flows. In H. Hauser, S. Strassburger, and H. Theisel, editors, Simulation and Visualization 2008 (Proceedings), pages 107 – 120, 2008.
D. J. Higham. Highly continuous runge-kutta interpolants. ACM Trans. Math. Softw., 17(3):368–386, 1991.
E. Hairer, S. P. Nørsett, and G. Wanner. Solving Ordinary Differential Equations I, second edition, volume 8 of Springer Series in Comput. Mathematics. Springer-Verlag, 1993.
E. Hughes, B. Taccardi, and F.B. Sachse. A heuristic streamline placement technique for visualization of electrical current flow. J. Flow Visualization and Image Processing, to appear, 2006.
J. P. M. Hultquist. Constructing stream surfaces in steady 3d vector fields. In A. E. Kaufman and G. M. Nielson, editors, Proceedings of IEEE Visualization 1992, pages 171 – 178, Boston, MA, 1992.
V. Interrante and C. Grosch. Visualizing 3d flow. IEEE Computer Graphics and Applications, 8(4):49–53, 1998.
T. Inanc, S.C. Shadden, and J.E. Marsden. Optimal trajectory generation in ocean flows. In Proceedings of the American Control Conference, pages 674–679, 2005.
M. Jiang, R. Machiraju, and D. Thompson. Geometric verification of swirling features in flow fields. In IEEE Visualization Proceedings, pages 307 – 314, 2002.
R. S. Laramee, C. Garth, J. Schneider, and H. Hauser. Texture advection on stream surfaces: A novel hybrid visualization applied to cfd simulation results. In Data Visualization, Proceedings of the Joint EUROGRAPHICS - IEEE VGTC Symposium on Visualization (EuroVis 2006), 2006.
H. Löffelmann, L. Mroz, E. Gröller, and W. Purgathofer. Stream arrows: enhancing the use of stream surfaces for the visualization of dynamical systems. The Visual Computer, 13(8):359 – 369, 1997.
M. Langbein, G. Scheuermann, and X. Tricoche. An efficient point location method for visualization in large unstructured grids. In Proceedings of Vision, Modeling, Visualization, 2003.
O. Mallo, R. Peikert, C. Sigg, and F. Saldo. Illuminated streamlines revisited. In Proceedings of IEEE Visualization 2005, pages 19–26, October 2005.
P. J. Prince and J. R. Dormand. High order embedded runge-kutta formulae. Journal of Computational and Applied Mathematics, 7(1), 1981.
L. F. Shampine. Interpolation for Runge-Kutta methods. SIAM J. Numer. Anal., 5, 1985.
I. A. Sadarjoen and F. H. Post. Geometric methods for vortex extraction. In Joint Eurographics-IEEE TVCG Symposium on Visualization, pages 53 – 62, 1999.
T. Salzbrunn and G. Scheuermann. Streamline predicates. IEEE Transactions on Visualization and Computer Graphics, 12(6):1601–1612, 2006.
D. Stalling, M. Zöckler, and H.-C. Hege. Fast display of illuminated field lines. IEEE Transactions on Visualization and Computer Graphics, 3(2):118–128, 1996.
X. Tricoche, C. Garth, T. Bobach, G. Scheuermann, and M. Ruetten. Accurate and efficient visualization of flow structures in a delta wing simulation. In Proceedings of 34th AIAA Fluid Dynamics Conference and Exhibit, AIAA Paper 2004-2153, 2004.
X. Tricoche, C. Garth, G. Kindlmann, E. Deines, G. Scheuermann, M. Rütten, and C. Hansen. Visualization of intricate flow structures for vortex breakdown analysis. In Proceeding of IEEE Visualization ’04 Conference, pages 187–194, 2004.
X. Tricoche, C. Garth, and G. Scheuermann. Fast and robust extraction of separation line features. In Scientific Visualization: The Visual Extraction of Knowledge from Data, pages 245–263. Mathematics + Visualization, Springer, 2005.
X. Tricoche and C. Garth. Topological methods for visualizing vortical flows. In Mathematical Foundations of Visualization, Computer Graphics, and Massive Data Exploration. 2006
J.J. van Wijk. Implicit stream surfaces. In Proceedings of IEEE Visualization ’93 Conference, pages 245–252, 1993.
A. Wiebel. Tetrahedrization of irregular grids and 3d helmholtz-hodge decomposition of vector fields. Project Thesis, Dept. of Computer Science, University of Kaiserslautern, 2003.
R. Westermann, C. Johnson, T. Ertl: A level-set method for flow visualization. IEEE Visualization 2000: 147-154
X. Ye, D. Kao, and A. Pang. Strategy for seeding 3d streamlines. In IEEE Computer Society Press, editor, IEEE Visualization Proceedings 2005, pages 471–478, October 2005.

Lagrangian Visualization

E. Aurell, G. Boffetta, A. Crisanti, G. Paladin, A. Vulpiani. Predictability in the large: an extension of the concept of lyapunov exponent. J. Phys. A: Math. Gen, 30:1.26, 1997.
M. S. Chong, A. E. Perry, B. J. Cantwell. A general classification of three-dimensional flow field. Phys. Fluids A 2, 765, 1990.
D. Eberly. Ridges in Image and Data Analysis. Computational Imaging and Vision. Kluwer Academic Publishers, 1996.
R. Fuchs, R. Peikert, H. Hauser, F. Sadlo, P. Muigg. Parallel Vectors Criteria for Unsteady Flow Vortices. IEEE Transactions on Visualization and Computer Graphics, Vol. 14, No. 3, pp. 615-626, 2008.
R. Fuchs, R. Peikert, F. Sadlo, B. Alsallakh, E. Gröller. Delocalized Unsteady Vortex Region Detectors. Proceedings VMV 2008, pp. 81-90, 2008.
C. Garth, F. Gerhardt, X. Tricoche, H. Hagen. Efficient Computation and Visualization of Coherent Structures in Fluid Flow Applications, In Proceeding of IEEE Visualization 2007, pp. 1464-1471, 2007.
J. C. R. Hunt. Vorticity and vortex dynamics in complex turbulent flows. In Proc. CANCAM, Trans. Can. SOC. Mech. Engrs 11, 21. 1987.
G. Haller. Finding finite-time invariant manifolds in two-dimensional velocity fields. Chaos 10, 99–108, 2000.
G. Haller. Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D 149, 248–277, 2001.
G. Haller. An objective definition of a vortex. Journal of Fluid Mechanics, 525:1–26, 2005.
J. Helman, L. Hesselink. Representation and display of vector field topology in fluid flow data sets. Computer 22, 8, 27–36, 1989.
J. Jeong, F. Hussain. On the identification of a vortex. Journal of Fluid Mechanics, 285:69–84, 1995.
S. K. Robinson. Coherent Motions in the Turbulent Boundary Layer. Ann. Rev. Fluid Mechanics, 23:601-639, 1991.
M. Roth, R. Peikert. A higher-order method for finding vortex core lines. In Proceedings IEEE Visualization 1998, 143–150, 1998.
F. Sadlo, R. Peikert, M. Sick. Visualization Tools for Vorticity Transport Analysis in Incompressible Flow. IEEE Transactions on Visualization and Computer Graphics, Vol. 12, No. 5, pp. 949-956 2006.
F. Sadlo, R. Peikert. Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction. IEEE Transactions on Visualization and Computer Graphics, Vol. 13, No. 6, pp. 1456-1463, 2007.
F. Sadlo, D. Weiskopf. Time-Dependent 2D Vector Field Topology: An Approach Inspired by Lagrangian Coherent Structures. Computer Graphics Forum, accepted for publication, 2010.
J. Sahner, T. Weinkauf, H. C. Hege. Galilean Invariant Extraction and Iconic Representation of Vortex Core Lines. In EuroVis 2005, 151-160, 2005.
S. C. Shadden. Lagrangian coherent structures. http://www.cds.caltech.edu/~shawn/LCS-tutorial/contents.html, 2005.
T. Schafhitzel, J. Vollrath, J. Gois, D. Weiskopf, A. Castelo, T. Ertl. Topology-Preserving lambda2-based Vortex Core Line Detection for Flow Visualization. Computer Graphics Forum (Eurovis 2008) , 27(3):1023-1030, 2008.
D. Sujudi and R. Haimes. Identification of swirling flow in 3D vector fields. Technical Report AIAA-95-1715, American Institute of Aeronautics and Astronautics, 1995.
T. Weinkauf, J. Sahner, H. Theisel, H.-C. Hege. Cores of Swirling Particle Motion in Unsteady Flows. IEEE Transactions on Visualization and Computer Graphics, 13(6), 2007.

Large Data and Parallel Visualization

coming soon...

Flow Visualization Applications in Biomedicine

N. Andrysco and X. Tricoche. Matrix Trees. Computer Graphics Forum (Proceedings of EuroVis 2010), 29(3), 2010.
D. Arora, M. Behr, and M. Pasquali. A Tensor-Based Measure for Estimating Blood Damage. Artificial Organs, 28(11):1002–1015, 2004.
D. Arora, M. Behr, and M. Pasquali. Hemolysis Estimation in a Centrifugal Blood Pump Using a Tensor-Based Measure. Artificial Organs, 30(7):539–547, 2006.
C. Garth and K. I. Joy: Fast, Memory-Efficient Cell Location in Unstructured Grids for Visualization. To appear in IEEE Transactions on Visualization and Computer Graphics, 16(6), 2010.
B. Hentschel, I. Tedjo-Palczynski, M. Probst, M. Wolter, M. Behr, C. Bischof, and T. Kuhlen. Interactive Blood Damage Analysis for Ventricular Assist Devices. IEEE Transactions on Visualization and Computer Graphics, 14(6), pp. 1515-1522, 2008.
M. Langbein, G. Scheuermann, and X. Tricoche. An Efficient Point Location Method for Visualization in Large Unstructured Grids. In Proceedings of Vision, Modeling, and Visualization (VMV), pp. 27-35, 2003.
D. Pugmire, H. Childs, C. Garth, S. Ahern, and G. Weber. Scalable Computation of Streamlines on Very Large Datasets. In Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis, 2009.
M. Schirski, A. Gerndt, T. van Reimersdahl, T. Kuhlen, P. Adomeit, O. Lang, S. Pischinger, and C.Bischof. ViSTA FlowLib - A Framework for Interactive Visualization and Exploration of Unsteady Flows in Virtual Environments. In Proceedings of the International Immersive Projection Technologies Workshop and 9th Eurographics Workshop on Virtual Environments, pp. 77-852003.
M. Wolter, I. Assenmacher, B. Hentschel, M. Schirski, and T. Kuhlen. A Time Model for Time-Varying Visualization. Computer Graphics Forum, 28(6), pp. 1561-1571, 2009.
K. Bürger, J. Schneider, P. Kondratieva, J. Krüger, and R. Westermann. Interactive Visual Exploration of Unsteady 3D Flows. Proceedings of the Joint EG/IEEE VGTC Symposium on Visualization', pp. 251--258, 2007.
D. Ellsworth, B. Green, P. Moran. Interactive Terascale Particle Visualization. Proceedings of IEEE Visualization, pp. 353--360, 2004.
J. Krüger, P. Kipfer, P. Kondratieva, R. Westermann. A Particle System for Interactive Visualization of 3D Flows. IEEE Transactions on Visualization and Computer Graphics (11:6), pp. 744--756, 2005.
F. Kuester, R. Bruckschen, B. Hamann, K. I. Joy. Visualization of Particle Traces in Virtual Environments Proceedings of ACM Symposium on Virtual Reality Software and Technology (VRST), 2001.
M. Schirski, C. Bischof, and T. Kuhlen. Interactive Exploration of Large Data in Hybrid Visualization Environments. Proceedings of the 13th Eurographics Symposium on Virtual Environments and 10th Immersive Projection Technology Workshop', pp. 69-76, 2007.
M. Schirski, T. Kuhlen, M. Hopp, P. Adomeit, S. Pischinger, C. Bischof. Virtual Tubelets - Efficiently Visualizing Large Amounts of Particle Trajectories. Computers and Graphics (29:1), pp. 17-27, 2005.