Lagrangian coherent vortex structures and their numerical visualization

Authors

DOI:

https://doi.org/10.26089/NumMet.v19r328

Keywords:

computational fluid dynamics, scientific visualization, vortex, Lagrangian turbulence, chaotic advection, Poincar’e section, Lyapunov exponent

Abstract

Some issues related to the implementation and physico-mathematical support of computational experiments on the study of fluid and gas flows containing Lagrangian coherent vortex structures are considered. Methods and tools designed to visualize the vortex flows arising in various practical applications are discussed. Examples of visual representation of solutions to gas dynamics problems computed with Lagrangian approaches to the description of fluid and gas flows are given. In addition to the traditional approaches to the visualization of vortex flows based on the construction of contour curves of various flow quantities, the phase trajectories of Lagrangian particles, the Poincar’e sections, and the local Lyapunov exponent method are applied.

Author Biographies

K.N. Volkov

D.F. Ustinov Baltic State Technical University «Voenmekh»
• Professor

V.N. Emelyanov

D.F. Ustinov Baltic State Technical University «Voenmekh»
• Professor

I.E. Kapranov

D.F. Ustinov Baltic State Technical University «Voenmekh»
• Researcher

I.V. Teterina

D.F. Ustinov Baltic State Technical University «Voenmekh»
• Associate Professor

References

  1. A. E. Bondarev and V. A. Galaktionov, “Current Visualization Trends in CFD Problems,” Appl. Math. Sci. 8 (28), 1357-1368 (2014).
  2. K. N. Volkov, V. N. Emel’yanov, I. V. Teterina, and M. S. Yakovchuk, “Visualization of Vortical Flows in Computational Fluid Dynamics,” Zh. Vychisl. Mat. Mat. Fiz. 57 (8), 1374-1391 (2017) [Comput. Math. Math. Phys. 57 (8), 1360-1375 (2017)].
  3. M. A. Green, C. W. Rowley, and G. Haller, “Detection of Lagrangian Coherent Structures in Three-Dimensional Turbulence,” J. Fluid Mech. 572, 111-120 (2007).
  4. G. Haller, “Lagrangian Coherent Structures,” Annu. Rev. Fluid Mech. 47, 137-162 (2015).
  5. Y. Huang and M. A. Green, “Detection and Tracking of Vortex Phenomena Using Lagrangian Coherent Structures,” Exp. Fluids 56 (7), 1-12 (2015).
  6. H. J854nicke and G. Scheuermann, “Measuring Complexity in Lagrangian and Eulerian Flow Descriptions,” Comput. Graph. Forum 29 (6), 1783-1794 (2010).
  7. M. R. Allshouse and T. Peacock, “Lagrangian Based Methods for Coherent Structure Detection,” Chaos 25 (2015).
    doi 10.1063/1.4922968
  8. A. Hadjighasem, D. Karrasch, H. Teramoto, and G. Haller, “Spectral-Clustering Approach to Lagrangian Vortex Detection,” Phys. Rev. E 93 (2016).
    doi 10.1103/PhysRevE.93.063107
  9. K. L. Schlueter-Kuck and J. O. Dabiri, “Coherent Structure Colouring: Identification of Coherent Structures from Sparse Data Using Graph Theory,” J. Fluid Mech. 811, 468-486 (2017).
  10. K. V. Koshel and S. V. Prants, “Chaotic Advection in the Ocean,” Usp. Fiz. Nauk 176 (11), 1177-1206 (2006) [Phys. Usp. 49 (11), 1151-1178 (2006)].
  11. X. Yuan and B. Chen, “Illustrating Surfaces in Volume,” in Proc. 6th Joint IEEE/EG Symp. on Visualization, Konstanz, Germany, May 19-21, 2004 (Eurographics Association, Aire-la-Ville, 2004), pp. 9-16.
  12. K. Bürger, P. Kondratieva, J. Krüger, and R. Westermann, “Importance-Driven Particle Techniques for Flow Visualization,” in Proceedings IEEE Pacific Visualization Symposium, Kyto, Japan, March 4-7, 2008 (IEEE Press, New York, 2008), pp. 71-78.
  13. K. Liang, P. Monger, and H. Couchman, “Interactive Parallel Visualization of Large Particle Datasets,” Parallel Comput. 31 (2), 243-260 (2005).
  14. C. Jones and K.-L. Ma, “Visualizing Flow Trajectories Using Locality-based Rendering and Warped Curve Plots,” IEEE Trans. Vis. Comput. Graph. 16 (6), 1587-1594 (2010).
  15. F. Sadlo, S. Bachthaler, C. Dachsbacher, and D. Weiskopf, “Space-Time Flow Visualization of Dynamics in 2D Lagrangian Coherent Structures,” in Computer Vision, Imaging and Computer Graphics. Theory and Application (Springer, Berlin, 2013), pp. 145-159.
  16. O. G. Bakunin, “Stochastic Instability and Turbulent Transport. Characteristic Scales, Increments, and Diffusion Coefficients,” Usp. Fiz. Nauk 185 (3), 271-306 (2015) [Phys. Usp. 58 (3), 252-285 (2015)].
  17. A. Pobitzer, R. Peikert, R. Fuchs, et al., “On the Way Towards Topology-Based Visualization of Unsteady Flow - the State of the Art,” in EuroGraphics 2010 State of the Art Reports, Norrköping, Sweden, May 3-7, 2010 (Blackwell Publishing, Hoboken, 2010), pp. 137-154.
  18. S. C. Shadden, F. Lekien, and J. E. Marsden, “Definition and Properties of Lagrangian Coherent Structures from Finite-Time Lyapunov Exponents in Two-Dimensional Aperiodic Flows,” Physica D 212 (3-4), 271-304 (2005).
  19. T. Lindeberg, “Feature Detection with Automatic Scale Selection,” Int. J. Comput. Vis. 30 (2), 79-116 (1998).
  20. B. Schindler, R. Peikert, R. Fuchs, and H. Theisel, “Ridge Concepts for the Visualization of Lagrangian Coherent Structures,” in Topological Methods in Data Analysis and Visualization II (Springer, Berlin, 2012), pp. 221-235.
  21. E. Aurell, G. Boffetta, A. Crisanti, et al., “Predictability in the Large: An Extension of the Concept of Lyapunov Exponent,” J. Phys. A: Math. Gen. 30 (1), 1-26 (1997).
  22. D. Karrasch and G. Haller, “Do Finite-Size Lyapunov Exponents Detect Coherent Structures?,” Chaos 23 (2013).
    doi 10.1063/1.4837075
  23. G. Boffetta, G. Lacorata, G. Redaelli, and A. Vulpiani, “Detecting Barriers to Transport: A Review of Different Techniques,” Physica D 159 (1-2), 58-70 (2001).
  24. F. Sadlo and R. Peikert, “Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction,” IEEE Trans. Vis. Comput. Graph. 13 (6), 1456-1463 (2007).
  25. R. Peikert, A. Pobitzer, F. Sadlo, and B. Schindler, “A Comparison of Finite-Time and Finite-Size Lyapunov Exponents,” in Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization (Springer, Berlin, 2014), pp. 187-200.
  26. M. Cencini and A. Vulpiani, “Finite Size Lyapunov Exponent: Review on Applications,” J. Phys. A. Math. Theor. 46 (2013).
    doi 10.1088/1751-8113/46/25/254019
  27. M. V. Budyansky and S. V. Prants, “A Mechanism of Chaotic Mixing in an Elementary Deterministic Flow,” Pis’ma Zh. Tekh. Fiz. 27 (12), 51-56 (2001) [Tech. Phys. Lett., 27 (6), 508-510 (2001)].
  28. A. Kuhn, Ch. Rössl, T. Weinkauf, and H. Theisel, “A Benchmark for Evaluating FTLE Computations,” in Proc. Pacific Visualization Symposium (PacificVis), Songdo, Korea, February 22-March 2, 2012 (IEEE Computer Society, Piscataway, 2012).
    doi 10.1109/PacificVis.2012.6183582
  29. J. M. Nese, “Quantifying Local Predictability in Phase Space,” Physica D 35 (1-2), 237-250 (1989).
  30. J. Kasten, C. Petz, I. Hotz, et al., “Localized Finite-time Lyapunov Exponent for Unsteady Flow Analysis,” in Vision Modeling and Visualization (Univ. of Magdeburg, Magdeburg, 2009), Vol. 1, pp. 265-274.
  31. F. Lekien and S. D. Ross, “The Computation of Finite-Time Lyapunov Exponents on Unstructured Meshes and for Non-Euclidean Manifolds,” Chaos 20 (2010).
    doi 10.1063/1.3278516
  32. M. Van Dyke, An Album of Fluid Motion (Parabolic Press, Stanford, 1982; Mir, Moscow, 1986).
New computational technologies

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Published

26-12-2018

How to Cite

Волков К., Емельянов В., Капранов И., Тетерина И. Lagrangian Coherent Vortex Structures and Their Numerical Visualization // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2018. 19. 293-313. doi 10.26089/NumMet.v19r328

Issue

Vol. 19 (2018): Issue 3.

Section

Section 1. Numerical methods and applications

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