Interactive Exploration of Stress Tensors Used in Computational Turbulent Combustion

  • Adrian Maries
  • Abedul Haque
  • S. Levent Yilmaz
  • Mehdi B. Nik
  • G. Elisabeta Marai
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


Simulation and modeling of turbulent flow, and of turbulent reacting flow in particular, involves solving for and analyzing time-dependent and spatially dense tensor quantities, such as turbulent stress tensors. The interactive visual exploration of these tensor quantities can effectively steer the computational modeling of combustion systems. In this chapter, we discuss the challenges in dense symmetric-tensor visualization applied to turbulent combustion calculation, and analyze the feasibility of using several established tensor visualization techniques in the context of exploring space-time relationships in computationally-simulated combustion tensor data. To tackle the pervasive problems of occlusion and clutter, we propose a solution combining techniques from information and scientific visualization. Specifically, the proposed solution combines a detailed 3D inspection view based on volume rendering with glyph-based representations—used as 2D probes—while leveraging interactive filtering and flow salience cues to clarify the structure of the tensor datasets. Side-by-side views of multiple timesteps facilitate the analysis of time-space relationships. The resulting prototype enables an analysis style based on the overview first, zoom and filter, then details on demand paradigm originally proposed in information visualization. The result is a visual analysis tool to be utilized in debugging, benchmarking, and verification of models and solutions in turbulent combustion. We demonstrate this analysis tool on three example configurations and report feedback from combustion researchers.


Large Eddy Simulation Direct Numerical Simulation Tensor Field Turbulent Combustion Bunsen Burner 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Acknowledgements to the Pitt Visualization Research group and to NSF-IIS-0952720.


  1. 1.
    Bhalerao, A., Westin, C.-F.: Tensor splats: visualising tensor fields by texture mapped volume rendering. In: Proceedings of Sixth International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI ’03), Montréal, pp. 294–901 (2003)Google Scholar
  2. 2.
    Card, S.K., Mackinlay, J.D., Shneiderman, B.: Readings in Information Visualization: Using Vision to Think. Morgan Kaufmann, San Francisco (1999)Google Scholar
  3. 3.
    Chen, W., Ding, Z., Zhang, S., MacKay-Brandt, A., Correia, S., Qu, H., Crow, J.A., Tate, D.F., Yan, Z., Peng, Q.: A novel interface for interactive exploration of DTI fibers. IEEE Trans. Vis. Comput. Graph. 15(6), 1433–1440 (2009)Google Scholar
  4. 4.
    Chen, Y., Peters, N., Schneemann, G.A., Wruck, N., Renz, U., Mansour, M.S.: The detailed flame structure of highly stretched turbulent premixed methane-air flames. Combust. Flame 107, 223–226 (1996)Google Scholar
  5. 5.
    Ciofalo, M.: Large Eddy Simulation: a ritical survey of models and applications. In: Advances in Heat Transfer, vol. 25, pp. 321–419. Academic, New York (1994)Google Scholar
  6. 6.
    Cox, A., Xaquin, G.V., Leonhardt, D.: How this bear market compares. (2008), last accessed July 4th 2012
  7. 7.
    Dick, C., Georgii, J., Burgkart, R., Westermann, R.: Stress tensor field visualization for implant planning in orthopedics. IEEE Trans. Vis. Comput. Graph. 15(6), 1399–1406 (2009)Google Scholar
  8. 8.
    Dunn-Rankin, D. (ed.): Lean Combustion: Technology and Control. Academic, New York (2008)Google Scholar
  9. 9.
    Fox, R.O.: Computational models for turbulent reacting flows. Cambridge University Press, Cambridge (2003)Google Scholar
  10. 10.
    Givi, P.: Filtered density function for subgrid scale modeling of turbulent combustion. AIAA J. 44(1), 16–23 (2006)Google Scholar
  11. 11.
    Hack, R.L., McDonell, V.G.: Impact of ethane, propane, and diluent content in natural gas on the performance of a commercial microturbine generator. J. Eng. Gas Turb. Power 130(1), 011509 (2008)Google Scholar
  12. 12.
    Haworth, D.C.: Progress in probability density function methods for turbulent reacting flows. Prog. Energ. Combust. vol. 36, pp. 168–259 (2010)Google Scholar
  13. 13.
    Jeremic, B., Scheuermann, G., Frey, J., Yang, Z., Hamann, B., Joy, K.I., Hagen, H.: Tensor visualizations in computational geomechanics. Int. J. Numer. Anal. Methods Geomech. 26(10), 925–944 (2002)Google Scholar
  14. 14.
    Jianu, R., Demiralp, C., Laidlaw, D.H.: Exploring 3D DTI fiber tracts with linked 2D representations. IEEE Trans. Vis. Comput. Graph. 15(6), 1449–1456 (2009)Google Scholar
  15. 15.
    Johnsen, E., Larsson, J., Bhagatwala, A.V., Cabot, W.H., Moin, P., Olson, B.J., Rawat, P.S., Shankar, S.K., Sjogreen, B., Yee, H., Zhong, X., Lele, S.K.: Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves. J Comput. Phys. 229(4), 1213–1237 (2010)Google Scholar
  16. 16.
    Kang, S., Iaccarino, G., Ham, F. and Moin, P.: Prediction of wall-pressure fluctuation in turbulent flows with an immersed boundary method. J Comput. Phys. 228, 6753–6772 (2009)Google Scholar
  17. 17.
    Kindlmann, G.: Superquadric tensor glyphs. In: Proceedings of IEEE TVCG/EG Symposium on Visualization 2004, pp. 147–154 (2004)Google Scholar
  18. 18.
    Kindlmann, G., Westin, C.-F.: Diffusion tensor visualization with glyph packing. IEEE Trans. Vis. Comput. Graph. 12(5), 1329–1336 (2006)Google Scholar
  19. 19.
    Kindlmann, G., Weinstein, D., Hart, D.: Strategies for direct volume rendering of diffusion tensor fields. IEEE Trans. Vis. Comput. Graph. 6(2) 124–138 (2000)Google Scholar
  20. 20.
    Kuo, K.: Principles of Combustion. Wiley, Hoboken (2005)Google Scholar
  21. 21.
    Lesieur, M., Metais, O.: New Trends in Large Eddy Simulations of Turbulence. Ann. Rev. Fluid Mech. 28, 45–82 (1996)Google Scholar
  22. 22.
    Peters, N.: Turbulent Combustion. Cambridge University Press, Cambridge (2000)Google Scholar
  23. 23.
    Poinsot, T., Veynante, D.: Theoretical and Numerical Combustion, 2nd edn. R.T. Edwards, Inc., Philadelphia (2005)Google Scholar
  24. 24.
    Pope, S.B.: Turbulent Flows, Cambridge University Press, Cambridge (2000)Google Scholar
  25. 25.
    Pope, S.B.: Advances in PDF methods for turbulent reactive flows. In: Andersson, H.I., Krogstad, P.A. (eds.) Advances in Turbulence X, pp. 529–536. CIMNE, Barcelona (2004)Google Scholar
  26. 26.
    Rhyne, T., Tory M., Munzner, T., Ward, M., Johnson, C., Laidlaw, D.: Information and scientific visualization: separate but equal or happy together at last? IEEE Visualization (Panel Proceedings), pp. 611–614. Seattle, WA (2003)Google Scholar
  27. 27.
    Robertson, G., Fernandez, R., Fisher, D., Lee, B., Stasko, J.: Effectiveness of animation in trend visualization. IEEE Trans. Vis. Comput. Graph. 14(6), 1325–1332 (2008)Google Scholar
  28. 28.
    Richards, G.A., McMillian, M.M., Gemmen, R.S., Rogers, W.A., Cully, S.R.: Issues for low-emission, fuel-flexible power systems. Prog. Energy Combust. Sci. 27(2), 141–169 (2001)Google Scholar
  29. 29.
    Sankaran, R., Hawkes, E.R., Chen, J.H., Lu, T., Law, C.K.: Structure of a spatially developing turbulent lean methane-air bunsen flame. Proc. Combust. Inst. 31, 1291–1298 (2007)Google Scholar
  30. 30.
    Sherbondy, A., Akers, D., Mackenzie, R., Dougherty, R., Wandell, B.: Exploring connectivity of the brain’s white matter with dynamic queries. IEEE Trans. Vis. Comput. Graph. 11(4), 419–430 (2005)Google Scholar
  31. 31.
    Slavin, V., Pelcovits, R., Loriot, G., Callan-Jones, A., Laidlaw, D.: Techniques for the visualization of topological defect behavior in nematic liquid crystals. IEEE Trans. Vis. Comput. Graph. 12(5), 1323–1328 (2006)Google Scholar
  32. 32.
    Vreman, A., van Oijen, J., de Goey, L., Bastiaans, R.: Direct numerical simulation of hydrogen addition in turbulent premixed Bunsen flames using flamelet-generated manifold reduction. Int. J. Hydrog. Energy. 34, 2778–2788 (2009)Google Scholar
  33. 33.
    Tannehill, J.C., Anderson, D.A., Pletcher, R.H.: Computational Fluid Mechanics and Heat Transfer, 2nd edn. Taylor & Francis, Washington, DC (1997)Google Scholar
  34. 34.
    Tufte, E.R.: Envisioning Information. Graphics Press, Cheshire (1990)Google Scholar
  35. 35.
    Tufte, E.R.: Visual Explanations: Images and Quantities, Evidence and Narrative. Graphics Press, Cheshire (1997)Google Scholar
  36. 36.
    Tufte, E.R.: The Visual Display of Quantitative Information. Graphics Press, Cheshire (2001)Google Scholar
  37. 37.
    Wenger, A., Keefe, D.F., Zhang, S., Laidlaw, D.H.: Interactive volume rendering of thin thread structures within multivalued scientific data sets. IEEE Trans. Vis. Comput. Graph. 10(6), 664–672 (2004)Google Scholar
  38. 38.
    Westin, C.-F., Maier, S.E., Mamata, H., Nabavi, A., Jolesz, F.A., Kikinis, R.: Processing and visualization for diffusion tensor mri. Med. Image Anal. 6, 93–108 (2002)Google Scholar
  39. 39.
    Yilmaz, S.L., Nik, M.B., Givi, P., Strakey, P.A.: Scalar filtered density function for large eddy simulation of a premixed bunser burner. J. Propul. Power. 26, 84–93 (2010)Google Scholar
  40. 40.
    Zhang, S., Demiralp, C., Laidlaw, D.H.: Visualizing diffusion tensor MR images using streamtubes and streamsurfaces. IEEE Trans. Vis. Comput. Graph. 9(4), 454–462 (2003)Google Scholar
  41. 41.
    Zhang, S., Kindlmann, G., Laidlaw, D.H.: Diffusion tensor MRI visualization. In: Visualization Handbook. Academic, Amsterdam (2004)Google Scholar
  42. 42.
    Zhang, E., Yeh, H., Lin, Z., Laramee, R.S.: Asymmetric tensor analysis for flow visualization. IEEE Trans. Vis. Comput. Graph. 15(1), 106–122 (2009)Google Scholar
  43. 43.
    Zheng, X., Pang, A.: Volume deformation for tensor visualization. In: Proceedings of the IEEE Visualization Conference ’02, pp. 379–386. Boston, MA (2002)Google Scholar
  44. 44.
    Zhukov, L., Barr, A.H.: Oriented tensor reconstruction: tracing neural pathways from diffusion tensor MRI. In Proceedings of the IEEE Visualization Conference ’02, pp. 387–394. Boston, MA (2002)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2012

Authors and Affiliations

  • Adrian Maries
    • 1
  • Abedul Haque
    • 1
  • S. Levent Yilmaz
    • 2
  • Mehdi B. Nik
    • 3
  • G. Elisabeta Marai
    • 1
  1. 1.Department of Computer ScienceUniversity of PittsburghPittsburghUSA
  2. 2.Center for Simulation and ModelingUniversity of PittsburghPittsburghUSA
  3. 3.Department of Mechanical Engineering and Materials ScienceUniversity of PittsburghPittsburghUSA

Personalised recommendations