The Community for Technology Leaders
RSS Icon
Issue No.02 - March/April (2010 vol.16)
pp: 1
G.H. Weber , Lawrence Berkeley Nat. Lab., Berkeley, CA, USA
V. Pascucci , Sci. Comput. & Imaging Inst., Univ. of Utah, Salt Lake City, UT, USA
M. Day , Lawrence Berkeley Nat. Lab., Berkeley, CA, USA
P.-T. Bremer , Center for Appl. Sci. Comput., Lawrence Livermore 'Nat. Lab., Livermore, CA, USA
This paper presents topology-based methods to robustly extract, analyze, and track features defined as subsets of isosurfaces. First, we demonstrate how features identified by thresholding isosurfaces can be defined in terms of the Morse complex. Second, we present a specialized hierarchy that encodes the feature segmentation independent of the threshold while still providing a flexible multiresolution representation. Third, for a given parameter selection, we create detailed tracking graphs representing the complete evolution of all features in a combustion simulation over several hundred time steps. Finally, we discuss a user interface that correlates the tracking information with interactive rendering of the segmented isosurfaces enabling an in-depth analysis of the temporal behavior. We demonstrate our approach by analyzing three numerical simulations of lean hydrogen flames subject to different levels of turbulence. Due to their unstable nature, lean flames burn in cells separated by locally extinguished regions. The number, area, and evolution over time of these cells provide important insights into the impact of turbulence on the combustion process. Utilizing the hierarchy, we can perform an extensive parameter study without reprocessing the data for each set of parameters. The resulting statistics enable scientists to select appropriate parameters and provide insight into the sensitivity of the results with respect to the choice of parameters. Our method allows for the first time to quantitatively correlate the turbulence of the burning process with the distribution of burning regions, properly segmented and selected. In particular, our analysis shows that counterintuitively stronger turbulence leads to larger cell structures, which burn more intensely than expected. This behavior suggests that flames could be stabilized under much leaner conditions than previously anticipated.
Hydrogen, Fires, Isosurfaces, Combustion, Robustness, User interfaces, Computer graphics, Information analysis, Numerical simulation, Statistical distributions, burning regions., Visualization, data analysis, topological data analysis, Morse complex, Reeb graph, feature detection, feature tracking, combustion simulations
G.H. Weber, V. Pascucci, M. Day, P.-T. Bremer, "Analyzing and Tracking Burning Structures in Lean Premixed Hydrogen Flames", IEEE Transactions on Visualization & Computer Graphics, vol.16, no. 2, pp. 1, March/April 2010, doi:10.1109/TVCG.2009.69
[1] P.K. Agarwal, H. Edelsbrunner, J. Harer, and Y. Wang, “Extreme Elevation on a 2-Manifold,” Discrete & Computational Geometry, vol. 36, no. 4, pp. 553-572, 2006.
[2] J.B. Bell, R.K. Cheng, M.S. Day, and I.G. Shepherd, “Numerical Simulation of Lewis Number Effects on Lean Premixed Turbulent Flames,” Proc. Combustion Inst., vol. 31, pp. 1309-1317, 2007.
[3] P. Bhaniramka, R. Wenger, and R. Crawfis, “Isosurface Construction in Any Dimension Using Convex Hulls,” IEEE Trans. Visualization and Computer Graphics, vol. 10, no. 2, pp. 130-141, Mar. 2004.
[4] P.-T. Bremer, H. Edelsbrunner, B. Hamann, and V. Pascucci, “A Topological Hierarchy for Functions on Triangulated Surfaces,” IEEE Trans. Visualization and Computer Graphics, vol. 10, no. 4, pp.385-396, July/Aug. 2004.
[5] P.-T. Bremer and V. Pascucci, “A Practical Approach to Two-Dimensional Scalar Topology,” Proc. Workshop Topology-Based Methods in Visualization (TopoInVis '07), pp. 151-171, 2007.
[6] A. Cayley, “On Contour and Slope Lines,” The London, Edinburgh and Dublin Philosophical Magazine and J. Science, vol. 18, pp. 264-268, 1859.
[7] M. Day, J. Bell, P.-T. Bremer, V. Pascucci, V. Beckner, and M. Lijewski, “Turbulence Effects on Cellular Burning Structures in Lean Premixed Hydrogen Flames,” Combustion and Flame, vol. 156, pp. 1035-1045, 2009.
[8] M.S. Day and J.B. Bell, “Numerical Simulation of Laminar Reacting Flows with Complex Chemistry,” Combustion Theory Modelling, vol. 4, no. 4, pp. 535-556, 2000.
[9] H. Edelsbrunner, M. Facello, and J. Liang, “On the Definition and the Construction of Pockets in Macromolecules,” Discrete Applied Math., vol. 88, nos. 1-3, pp. 83-102, 1998.
[10] H. Edelsbrunner and J. Harer, “Jacobi Sets of Multiple Morse Functions,” Foundations of Computational Math., Minneapolis 2002, pp. 37-57, Cambridge Univ. Press, 2002.
[11] H. Edelsbrunner, J. Harer, A. Mascarenhas, and V. Pascucci, “Time-Varying Reeb Graphs for Continuous Space-Time Data,” Proc. 20th Symp. Computational Geometry, pp. 366-372, 2004.
[12] H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci, “Morse-Smale Complexes for Piecewise Linear 3-Manifolds,” Proc. 19th Symp. Computational Geometry, pp. 361-370, 2003.
[13] H. Edelsbrunner, J. Harer, and A. Zomorodian, “Hierarchical Morse-Smale Complexes for Piecewise Linear 2-Manifolds,” Discrete & Computational Geometry, vol. 30, pp. 87-107, 2003.
[14] I. Fujishiro, R. Otsuka, S. Takahashi, and Y. Takeshima, “T-Map: A Topological Approach to Visual Exploration of Time-Varying Volume Data,” Proc. Sixth Int'l Symp. High Performance Computing, pp. 176-190, 2008.
[15] A. Gyulassy, M. Duchaineau, V. Natarajan, V. Pascucci, E. Bringa, A. Higginbotham, and B. Hamann, “Topologically Clean Distance Fields,” IEEE Trans. Computer Graphics and Visualization, vol. 13, no. 6, pp. 1432-1439, Nov. 2007.
[16] A. Gyulassy, V. Natarajan, V. Pascucci, P.-T. Bremer, and B. Hamann, “Topology-Based Simplification for Feature Extraction from 3D Scalar Fields,” IEEE Trans. Computer Graphics and Visualization, vol. 12, no. 4, pp. 474-484, 2006.
[17] A. Gyulassy, V. Natarajan, V. Pascucci, and B. Hamann, “Efficient Computation of Morse-Smale Complexes for Three-Dimensional Scalar Functions,” IEEE Trans. Computer Graphics and Visualization, vol. 13, no. 6, pp. 1440-1447, Nov./Dec. 2007.
[18] G. Ji and H.-W. Shen, “Efficient Isosurface Tracking Using Precomputed Correspondence Table,” Proc. Symp. Visualization (VisSym '04), pp. 283-292, 2004.
[19] G. Ji, H.-W. Shen, and R. Wegner, “Volume Tracking Using Higher Dimensional Isocontouring,” Proc. IEEE Visualization Conf., pp 209-216, 2003.
[20] E. Koutsofios and S. North, “Drawing Graphs with Dot,” Technical Report 910904-59113-08TM, AT&T Bell Laboratories, 1991.
[21] D. Laney, P.-T. Bremer, A. Mascarenhas, P. Miller, and V. Pascucci, “Understanding the Structure of the Turbulent Mixing Layer in Hydrodynamic Instabilities,” IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 5, pp. 1052-1060, Sept./Oct. 2006.
[22] J.C. Maxwell, “On Hills and Dales,” The London, Edinburgh and Dublin Philosophical Magazine and J. Science, vol. XL, pp. 421-427, 1870.
[23] J. Milnor, Morse Theory. Princeton Univ. Press, 1963.
[24] M. Morse, “Relations between the Critical Points of a Real Functions of N Independent Variables,” Trans. Am. Math. Soc., vol. 27, pp. 345-396, July 1925.
[25] L.R. Nackman, “Two-Dimensional Critical Point Configuration Graphs,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 4, pp. 442-450, July 1984.
[26] V. Pascucci, G. Scorzelli, P.-T. Bremer, and A. Mascarenhas, “Robust On-Line Computation of Reeb Graphs: Simplicity and Speed,” Proc. ACM SIGGRAPH, pp. 58.1-58.9, 2007.
[27] J. Pfaltz, “Surface Networks,” Geographical Analysis, vol. 8, pp. 77-93, 1976.
[28] G. Reeb, “Sur Les Points Singuliers D'une Forme De Pfaff Completement Intergrable Ou D'une Fonction Numerique [on the Singular Points of a Complete Integral Pfaff Form or of a Numerical Function],” Comptes Rendus Acad. Science Paris, vol. 222, pp. 847-849, 1946.
[29] F. Reinders, F.H. Post, and H.J.W. Spoelder, “Visualization of Time-Dependent Data with Feature Tracking and Event Detection,” The Visual Computer, vol. 17, no. 1, pp. 55-71, 2001.
[30] R. Samtaney, D. Silver, N. Zabusky, and J. Cao, “Visualizing Features and Tracking Their Evolution,” Computer, vol. 27, no. 7, pp. 20-27, July 1994.
[31] Y. Shinagawa, T.L. Kunii, H. Sato, and M. Ibusuki, “Modeling Contact of Two Complex Objects: With an Application to Characterizing Dental Articulations,” Computers and Graphics, vol. 19, no. 1, pp. 21-28, 1995.
[32] D. Silver and X. Wang, “Tracking and Visualizing Turbulent 3d Features,” IEEE Trans. Visualization and Computer Graphics, vol. 3, no. 2, pp. 129-141, Apr.-June 1997.
[33] D. Silver and X. Wang, “Tracking Scalar Features in Unstructured Datasets,” Proc. IEEE Visualization Conf., pp 79-86, 1998.
[34] B.-S. Sohn and C. Bajaj, “Time-Varying Contour Topology,” IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 1, pp. 14-25, Jan. 2006.
[35] A. Szymczak, “Subdomain-Aware Contour Trees and Contour Tree Evolution in Time-Dependent Scalar Fields,” Proc. Shape Modeling Int'l (SMI) Conf., pp. 136-144, 2005.
[36] G. Weber, P.-T. Bremer, J. Bell, M. Day, and V. Pascucci, “Feature Tracking Using Reeb Graphs,” Proc. Conf. Topology-Based Methods in Visualization (TopoInVis '09), 2009.
[37] X. Zhang and C. Bajaj, “Extraction, Visualization and Quantification of Protein Pockets,” Proc. Sixth Ann. Int'l Conf. Computational System Bioinformatics (CSB '07), pp. 275-286, 2007.
16 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool