UIA: a uniform integrated advection algorithm for steady and unsteady piecewise linear flow field on structured and unstructured grids

  • Fang Wang
  • Yang Liu
  • Dan Zhao
  • Liang Deng
  • Sikun Li
Regular Paper
  • 18 Downloads

Abstract

Integration-based geometric method is widely used in vector field visualization. To improve the efficiency of integration advection-based visualization, we propose a uniform integrated advection (UIA) algorithm on steady and unsteady vector field according to common piecewise linear field data set analysis. UIA employs cell gradient-based interpolation along spatial and temporal direction, and transforms multi-step advection into single-step advection in association with fourth-order Runge–Kutta advection process. UIA can significantly reduce computational load, and is applicable on arbitrary grid type with cell-center/cell-vertex data structure. The experiments are performed on steady/unsteady vector fields with two-dimensional cell-center unstructured grids and three-dimensional cell-vertex grids, and also on unsteady field from fluid dynamics numerical simulation. The result shows that the proposed algorithm can significantly improve advection efficiency and reduce visualization computational time compared with fourth-order Runge–Kutta.

Graphical abstract

Keywords

Scientific visualization Integration-based geometric method Unsteady vector field Piecewise linear GPU 

Notes

Acknowledgements

This work is supported by the National Key Research and Development Program of China (2016YFB0200701), Chinese 973 Program (2015CB-755604), and the National Natural Science Foundation of China (61202335).

References

  1. Anderson JDJ (2007) Computational fluid dynamics. China Machine, BeijingGoogle Scholar
  2. Anderson JDJ (2014) Fundamentals of aerodynamics, 5th edn. Aviation Industrial Publishing House, BeijingGoogle Scholar
  3. Barth T, Jespersen D (1989) The design and application of upwind schemes on unstructured meshes. AIAA Aerosp Sci Meet. doi: 10.2514/6.1989-366 Google Scholar
  4. Camp D, Garth C, Childs H, Pugmire D, Joy KI (2011) Streamline integration using mpi-hybrid parallelism on a large multicore architecture. IEEE Trans Visual Comput Gr 17(11):1702–1713. doi: 10.1109/tvcg.2010.259 CrossRefGoogle Scholar
  5. Camp D, Krishnan H, Pugmire D, Garth C, Johnson I, Bethel EW et al (2013) GPU acceleration of particle advection workloads in a parallel, distributed memory setting. In: Eurographics symposium on parallel graphics and visualization 2011, pp 1–8. Eurographics AssociationGoogle Scholar
  6. Chen W, Shen ZQ, Tao YB (2013) Data visualization. Publishing House of Electronics Industry, BeijingGoogle Scholar
  7. Coulliette C, Wiggins S (1999) Intergyre transport in a wind-driven, quasigeostrophic double gyre: an application of lobe dynamics. Nonlinear Process Geophys 7(1/2):59–85. doi: 10.5194/npg-8-69-2001 CrossRefGoogle Scholar
  8. Coulliette C, Lekien F, Paduan JD, Haller G, Marsden JE (2007) Optimal pollution mitigation in monterey bay based on coastal radar data and nonlinear dynamics. Environ Sci Technol 41(18):6562–6572. doi: 10.1021/es0630691 CrossRefGoogle Scholar
  9. Edmunds M, Laramee RS, Chen G, Max N, Zhang E, Ware C (2012) Surface-based flow visualization. Comput Gr 36(8):974–990. doi: 10.1016/j.cag.2012.07.006 CrossRefGoogle Scholar
  10. Haller G (2001) Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D-nonlinear Phenomena 149(4):248–277. doi: 10.1016/s0167-2789(00)00199-8 MathSciNetCrossRefMATHGoogle Scholar
  11. Haller G (2015) Lagrangian coherent structures. Annu Rev Fluid Mech 47(1):137–162. doi: 10.1146/annurev-fluid-010313-141322 CrossRefGoogle Scholar
  12. Hearn D, Baker M (1998) Computer graphics. Publishing House of Electronics Industry, BeijingMATHGoogle Scholar
  13. Jameson A, Schmidt W, Turkel E (1981) Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes. AIAA Fluid Plasma Dyn Conf. doi: 10.2514/6.1981-1259 Google Scholar
  14. Jiang GS, Shu CW (1996) Efficient implementation of weighted ENO schemes. J Comput Phys 126(1):202–228. doi: 10.1006/jcph.1996.0130 MathSciNetCrossRefMATHGoogle Scholar
  15. Kundu P, Cohen IM (2008) Fluid mechanics, 4th edn. Academic, ElsevierGoogle Scholar
  16. Laramee RS, Helwig H, Helmut D et al (2003) The state of the art in flow visualization: dense and texture-based techniques. Comput Gr Forum 22(2):203–221. doi: 10.1111/j.1467-8659.2004.00753.x Google Scholar
  17. Leung S (2011) An eulerian approach for computing the finite time lyapunov exponent. J Comput Phys 230(9):3500–3524. doi: 10.1016/j.jcp.2011.01.046 MathSciNetCrossRefMATHGoogle Scholar
  18. Lorendeau B, Fournier Y, Ribes A (2013) In-situ visualization in fluid mechanics using catalyst: a case study for code saturne. IEEE Symp Large Scale Data Anal Vis 2013:53–57. doi: 10.1109/ldav.2013.6675158 Google Scholar
  19. Ma KL, Wang C, Yu H, Tikhonova A (2007) In-situ processing and visualization for ultrascale simulations. J Phys Conf Ser 78:012043. doi: 10.1088/1742-6596/78/1/012043 CrossRefGoogle Scholar
  20. Ma QL, Xu HX, Zeng L, Cai X, Li SK (2010) Direct raycasting of unstructured cell-centered data by discontinuity roe-average computation. Vis Comput 26(6–8):1049–1059. doi: 10.1007/s00371-010-0447-9 CrossRefGoogle Scholar
  21. Mitchell C (1994) Improved reconstruction schemes for the Navier-Stokes equations on unstructured meshes. AIAA Pap. doi: 10.2514/6.1994-642 Google Scholar
  22. Murray L (2012) GPU acceleration of Runge–Kutta integrators. IEEE Trans Parallel Distrib Syst 23(1):94–101. doi: 10.1109/tpds.2011.61 CrossRefGoogle Scholar
  23. Nouanesengsy B, Lee TY, Shen HW (2011) Load-balanced parallel streamline generation on large scale vector fields. IEEE Trans Vis Comput Gr 17(12):1785–1794. doi: 10.1109/tvcg.2011.219 CrossRefGoogle Scholar
  24. Peterka T, Ross R, Nouanesengsy B, Lee TY, Shen HW, Kendall W et al (2011) A study of parallel particle tracing for steady-state and time-varying flow fields. IEEE Int Parallel Distrib Process Symp 2011:580–591. doi: 10.1109/ipdps.2011.62 Google Scholar
  25. Pobitzer A, Peikert R, Fuchs R, Schindler B, Kuhn A, Theisel H et al (2011) The state of the art in topology-based visualization of unsteady flow. Comput Gr Forum 30(6):1232–1239. doi: 10.1111/j.1467-8659.2011.01901.x CrossRefGoogle Scholar
  26. Post FH, Vrolijk B, Hauser H, Laramee RS, Doleisch H (2003) The state of the art in flow visualisation: feature extraction and tracking. Comput Gr Forum 22(4):775–792. doi: 10.1111/j.1467-8659.2003.00723.x CrossRefGoogle Scholar
  27. Shadden SC, Lekien F, Marsden JE (2005) Definition and properties of lagrangian coherent structures from finite-time lyapunov exponents in two-dimensional aperiodicflows. Physica D 212(3–4):271–304. doi: 10.1016/j.physd.2005.10.007 MathSciNetCrossRefMATHGoogle Scholar
  28. Shi K, Theisel H, Weinkauf T, Hege HC, Seidel HP (2008) Visualizing transport structures of time-dependent flow fields. IEEE Comput Gr Appl 28(5):24–36. doi: 10.1109/mcg.2008.106 CrossRefGoogle Scholar
  29. Tony ML, Laramee RS, Ronald P, Post FH, Min C (2010) Over two decades of integration-based, geometric flow visualization. Comput Gr Forum 29(6):1807–1829. doi: 10.1111/j.1467-8659.2010.01650.x CrossRefGoogle Scholar
  30. Ueng SK, Sikorski K, Ma KL (1995) Fast algorithms for visualing fluid motion in steady flow on unstructured grids. IEEE Conf Vis 1995:313–320. doi: 10.1109/visual.1995.485144 Google Scholar
  31. Ueng SK, Sikorski C, Ma KL (1996) Efficient streamline, streamribbon, and streamtube constructions on unstructured grids. IEEE Trans Vis Comput Gr 2(2):100–110. doi: 10.1109/2945.506222 CrossRefGoogle Scholar
  32. Wang WT, Wang WK, Li SK (2015) Batch advection for the piecewise linear vector field on simplicial grids. Comput Gr 54:75–83. doi: 10.1016/j.cag.2015.07.016 CrossRefGoogle Scholar

Copyright information

© The Visualization Society of Japan 2017

Authors and Affiliations

  1. 1.Computational Aerodynamics InstituteChina Aerodynamics Research and Development CenterMianyangChina
  2. 2.College of Computer ScienceNational University of Defense TechnologyChangshaChina

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