Flow visualization with strong and weak gas dynamic discontinuities in computational fluid dynamics


  • P.V. Bulat
  • K.N. Volkov
  • M.S. Yakovchuk


scientific visualization
computational fluid dynamics
flow visualization
shock wave


A number of methods for the visualization of flows with gas dynamic discontinuities are considered. These methods allow one to perform the direct comparison of numerical results with experimental data. Methods for the optical visualization of compressible gas flows (shadowgraphs, schlieren images, and interferograms) are discussed. Some examples illustrating the visual representation of numerical solutions of gas dynamics problems related to flows containing weak and strong gas dynamic discontinuities are given. Topological methods of visualization are applied to increase the visual representation of resulting images and to define the locations of critical points as well as the separation and attachment lines.





Section 1. Numerical methods and applications

Author Biographies

P.V. Bulat

K.N. Volkov

M.S. Yakovchuk


  1. K. N. Volkov, V. N. Emelyanov, I. V. Teterina, and M. S. Yakovchuk, “Methods and Concepts of Vortex Flow Visualization in the Problems of Computational Fluid Dynamics,” Vychisl. Metody Programm. 17, 81-100 (2016).
  2. K. N. Volkov, Yu. N. Deryugin, V. N. Emel’yanov, A. S. Kozelkov, and I. V. Teterina, Difference Schemes in Gas Dynamics on Unstructured Grids (Fizmatlit, Moscow, 2014) [in Russian].
  3. E. V. Vorozhtsov, Classification of Discontinuities in Gas Flows as the Pattern Recognition Problem , Preprint No. 23-86 (Khristianovich Inst. Theor. Appl. Mech., Novosibirsk, 1986).
  4. A. Hadjadj and A. Kudryavtsev, “Computation and Flow Visualization in High-Speed Aerodynamics,” J. Turbul. 6 (16), 33-81 (2005).
  5. R. Samtaney and N. J. Zabusky, “Visualization, Feature Extraction and Quantification of Numerical Visualizations of High-Gradient Compressible Flows,” in Flow Visualization. Techniques and Examples (Imperial College Press, London, 2000), pp. 317-344.
  6. S. B. Bazarov, “Application of Digital Image Processing for the Visualization of Gas-Dynamic Processes,” in Application of Scientific Visualization in Applied Problems (Mosk. Gos. Univ., Moscow, 2000), pp. 39-42.
  7. S. Cui, Y. Wang, X. Qian, and Z. Deng, “Image Processing Techniques in Shockwave Detection and Modeling,” J. Signal Inform. Process. 4 (3B), 109-113 (2013).
  8. Z. Wu, Y. Xu, W. Wang, and R. Hu, “Review of Shock Wave Detection Method in CFD Post-Processing,” Chin. J. Aeronaut. 26 (3), 501-513 (2013).
  9. J. J. Quirk and S. Karni, “On the Dynamics of a Shock-Bubble Interaction,” J. Fluid Mech. 318, 129-163 (1996).
  10. M. Anyoji and M. Sun, “Computer Analysis of the Schlieren Optical Setup,” in Proc. 27th Int. Congress on High-Speed Photography and Photonics, Xi’an, China, September 17-22, 2006 (SPIE Press, Bellingham, 2007), Vol. 6279.
    doi 10.1117/12.725101
  11. B. Atcheson, I. Ihrke, W. Heidrich, et al., “Time Resolved 3D Capture of Non-Stationary Gas Flows,” ACM Trans. Graph. 25 (5), 132-141 (2008).
  12. R. J. Schalkoff, Digital Image Processing and Computer Vision: An Introduction to Theory and Implementations (Wiley, New York, 1989).
  13. T. Kouchi, T. Hoshino, K. Sasaya, and G. Masuya, “Time-Space Trajectory of Unsteady Jet into Supersonic Crossflow Using High-Speed Framing Schlieren Images,” AIAA Paper (2009).
    doi 10.2514/6.2009-7316
  14. D. Estruch, N. J. Lawson, D. G. MacManus, et al., “Measurement of Shock Wave Unsteadiness Using a High-Speed Schlieren System and Digital Image Processing,” Rev. Sci. Instrum. 79, 126108-1-126108-3 (2008).
    doi 10.1063/1.3053361
  15. H. G. Pagendarm and B. Seitz, “An Algorithm for Detection and Visualization of Discontinuities in Scientific Data Fields Applied to Flow Data with Shock Waves,” in Scientific Visualization: Advanced Software Techniques (Ellis Horwood, New York, 1993), pp. 161-177.
  16. K.-L. Ma, J. V. Rosendale, and W. Vermeer, “3D Shock Wave Visualization on Unstructured Grids,” in Proc. Symp. on Volume Visualization, San Franсisco, USA, October 28-29, 1996 (IEEE Press, Piscataway, 1996), pp. 87-94.
  17. D. Lovely and R. Haimes, “Shock Detection from Computational Fluid Dynamics Results,” AIAA Paper (1999).
    doi 10.2514/6.1999-3285
  18. M. Kanamori and K. Suzuki, “Shock Wave Detection in Two-Dimensional Flow Based on the Theory of Characteristics from CFD Data,” J. Comput. Phys. 230 (8), 3085-3092 (2011).
  19. K. W. Morton and M. A. Rudgyard, “Shock Recovery and the Cell Vertex Scheme for the Steady Euler Equations,” in Lecture Notes in Physics (Springer, Heidelberg, 2005), Vol. 323, pp. 424-428.
  20. R. Haimes and D. Darmofal, “Visualization in Computational Fluid Dynamics: A Case Study,” in Proc. 2nd IEEE Conf. on Visualization, San Diego, USA, October 22-25, 1991 (IEEE Press, Los Alamitos, 1991), pp. 392-397.
  21. S. B. Bazarov, “Image processing in CFD,” in Proc. 8th Int. Conf. on Computer Graphics and Visualization (GraphiCon’98), Moscow, Russia, September 7-11, 1998 (Mosk. Gos. Univ., Moscow, 1998), pp. 258-264.
  22. S. Osher and R. Fedkiw, The Level Set Method and Dynamic Implicit Surfaces (Springer, New York, 2002).
  23. K. N. Volkov, V. N. Emelyanov, and M. S. Yakovchuk, “Numerical Simulation of the Interaction of a Transverse Jet with a Supersonic Flow Using Different Turbulence Models,” Zh. Prikl. Mekh. Tekh. Fiz. 56 (5), 64-75 (2015) [J. Appl. Mech. Tech. Phys. 56 (5), 789-798 (2015)].
  24. P. V. Bulat and K. N. Volkov, “Simulation of Supersonic Flow in a Channel with a Step on Nonstructured Meshes with the Use of the WENO Scheme,” Inzh. Fiz. Zh. 88 (4), 848-855 (2015) [J. Eng. Phys. Thermophys. 88 (4), 877-884 (2015)].
  25. P. V. Bulat and K. N. Volkov, “Use of WENO Schemes for Simulation of the Reflected Shock Wave-Boundary Layer Interaction,” Inzh. Fiz. Zh. 88 (5), 1163-1170 (2015) [J. Eng. Phys. Thermophys. 88 (5), 1203-1209 (2015)].