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Accuracy in 3D Particle Tracing

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Mathematical Visualization

Abstract

This paper presents a novel way of identifying and illustrating the accuracy in the particle tracing method for flow visualization. We make use of explicit Runge-Kutta methods for particle tracing in steady velocity fields, and describe three approaches to estimate the accuracy of the calculated path. These approaches are: re-integration (with smaller tolerance or in a backward direction), global error estimators and residuals in the velocity field. Visualization paradigms are also presented to convey data accuracy information and these ideas are implemented in an Open Inventor / IRIS Explorer environment.

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References

  1. R. Brankin, I. Gladwell, and L. Shampine, Rksuite: a suite of explicit runge-kutta codes for the initial value problem for odes softreport 91-s1, Tech. report, Department of Mathematics, Southern Methodist University, Dallas, TX 75275, USA, 1991.

    Google Scholar 

  2. K. Brodlie, A typology for scientific visualization, Visualization in Geographical Information Systems (H. Hearnshaw and D. Unwin, eds. ), John Wiley & Sons, 1994, pp. 34–41.

    Google Scholar 

  3. P. Buning, Sources of error in the graphical analysis of cfd results, Journal of Scientific Computing 3: 2 (1988), 149–164.

    Article  MathSciNet  MATH  Google Scholar 

  4. D. Darmofal and R. Haimes, An analysis of 3-d particle path integration algorithms, Journal of Computational Physics 123 (1995), 182–195.

    Article  Google Scholar 

  5. M. Goodchild, B. Buttenfield, and J. Wood, Introduction to visualizing data validity, Visualization in Geographical Information Systems (H. Hearnshaw and D. Unwin, eds. ), John Wiley & Sons, 1994, pp. 141–149.

    Google Scholar 

  6. R. Haber and D. Mcnabb, Visualization idioms: A conceptual model for scientific visualization systems, Visualization in Scientific Computing (G. Nielson, B. Shriver, and L. Rosenblum, eds. ), IEEE Computer Society Press, 1990, pp. 75–93.

    Google Scholar 

  7. D. Knight and G. Mallinson, Visualizing unstructured flow data using dual stream functions, IEEE Transaction on Visualization and Computer Graphics 2: 4 (1996), 355–363.

    Article  Google Scholar 

  8. S. Lodha, A. Pang, R. Sheehan, and C. Wittenbrink, Uflow: Visualizing uncertainty in fluid flow, Proceedings Visualization ‘86 (R. Yagel and G. Nielson, eds. ), ACM Press, 1996, pp. 249–254.

    Google Scholar 

  9. NAG, Iris explorer, URL http://www.nag.co.uk.

    Google Scholar 

  10. F. Post and T. van Walsum, Fluid flow visualization, Focus on Scientific Visualization, Springer Verlag, 1993, pp. 1–40.

    Google Scholar 

  11. L. Shampine and I. Gladwell, The next generation of runge-kutta codes, Computational Ordinary Differential Equations (J. Cash and I. Gladwell, eds. ), Oxford University Press, 1992, pp. 145–164.

    Google Scholar 

  12. L. Shampine and H. Watts, Global error estimation for ordinary differential equations, ACM Transactions on Mathematical Software 2: 2 (1976), 172–186.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Walton, Visualization benchmarking: A practical application of 3d publishing, 14th Eurographics UK Chapter Conference Proceedings, vol. 2, Imperial College of London, March 1996, pp. 339–351.

    Google Scholar 

  14. F. V. D. Wel, R. Hootsmans, and F. Ormeling, Visualization of data quality, Visualization in Modern Cartography (A. Maceachren and D. Taylor, eds.), Modern Cartography, vol. 2, Elsevier Science Ltd, 1994, pp. 313–331.

    Google Scholar 

  15. C. Wittenbrink, E. Saxon, J. Furman, A. Pang, and S. Lodha, Glyphs for visualizing uncertainty in environmental vector fields, SPIE & IS&T Conference Proceedings on Electronic Imaging: Visual Data Exploration and Analysis, vol. 2410, SPIE, February 1995, pp. 87–100.

    Google Scholar 

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© 1998 Springer-Verlag Berlin Heidelberg

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Lopes, A., Brodlie, K. (1998). Accuracy in 3D Particle Tracing. In: Hege, HC., Polthier, K. (eds) Mathematical Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03567-2_24

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  • DOI: https://doi.org/10.1007/978-3-662-03567-2_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08373-0

  • Online ISBN: 978-3-662-03567-2

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