Grid-free planar method of Particle Image Velocimetry




Particle Image Velocimetry, grid-free method, error, spatial resolution


Today, the method of PIV (Particle Image Velocimetry) is widely used in the field of experimental fluid mechanics due to its high reliability in solving practical problems. However, it has a known limitation associated with errors that occur when calculating velocity derivatives, which are necessary to deform the processed PIV images while improving the performance of the method. Since the number of errors increases with the use of higher order schemes, in practice it is most often limited to the first order, which in turn leads to a decrease in spatial resolution. In the present research, we propose a method that allows the schemes of more than the second order, which significantly improves the accuracy of measuring velocity and its derivatives, and thereby increases the spatial resolution. The method does not require the recovery of erroneous velocity vectors, avoids the numerical calculation of velocity derivatives, and is easily applied in practice.

Author Biographies

Dinar I. Zaripov

Mikhail P. Tokarev

Alexey A. Lukyanov

Dmitry M. Markovich


  1. M. P. Tokarev, D. M.  Markovich, and A. V. Bil’skii, “Adaptive Particle Image Processing Algorithms for Calculating Instantaneous Velocity Fields,” Vychisl. Tekhnol. 12 (3), 109-131 (2007).
  2. C. J. Kähler, T. Astarita, P. P. Vlachos, et al., “Main Results of the 4th International PIV Challenge,” Exp. Fluids 57 (6), 1-71 (2016).
    doi 10.1007/s00348-016-2173-1.
  3. M. Raffel, C. E. Willert, F. Scarano, et al., Particle Image Velocimetry: A Practical Guide (Springer, Cham, 2018).
  4. B. J. Kim and H. J. Sung, “A Further Assessment of Interpolation Schemes for Window Deformation in PIV,” Exp. Fluids 41 (3), 499-511 (2006).
    doi 10.1007/s00348-006-0177-y.
  5. M. P. Tokarev, Development of Algorithms and Software for Processing Images in Digital Tracer Visualization Methods , Candidate’s Dissertation in Technical Sciences (Institute of Thermophysics, Novosibirsk, 2010).
  6. H. T. Huang, H. E. Fiedler, and J. J. Wang, “Limitation and Improvement of PIV. Part I: Limitation of Conventional Techniques due to Deformation of Particle Image Patterns,” Exp. Fluids 15 (3), 168-174 (1993).
    doi 10.1007/BF00189883.
  7. H. T. Huang, H. E. Fiedler, and J. J. Wang, “Limitation and Improvement of PIV. Part II: Particle Image Distortion, a Novel Technique,” Exp. Fluids 15 (4), 263-273 (1993).
    doi 10.1007/BF00223404.
  8. F. Scarano, “Iterative Image Deformation Methods in PIV,” Meas. Sci. Technol. 13 (1), R1-R19 (2001).
    doi 10.1088/0957-0233/13/1/201.
  9. F. Scarano and M. L. Riethmuller, “Iterative Multigrid Approach in PIV Image Processing with Discrete Window Offset,” Exp. Fluids 26 (6), 513-523 (1999).
    doi 10.1007/s003480050318.
  10. F. Scarano and M. L. Riethmuller, “Advances in Iterative Multigrid PIV Image Processing,” Exp. Fluids 29 (Suppl 1), S051-S060 (2000).
    doi 10.1007/s003480070007.
  11. S. T. Wereley and C. D. Meinhart, “Second-Order Accurate Particle Image Velocimetry,” Exp. Fluids 31 (3), 258-268 (2001).
    doi 10.1007/s003480100281.
  12. L. Gui and J. M. Seiner, “An Improvement in the Nine-Point Central Difference Image Correction Method for Digital Particle Image Velocimetry Recording Evaluation,” Meas. Sci. Technol. 15 (10), 1958-1964 (2004).
    doi 10.1088/0957-0233/15/10/002.
  13. J. Westerweel, D. Dabiri, and M. Gharib, “The Effect of a Discrete Window Offset on the Accuracy of Cross-Correlation Analysis of Digital PIV Recordings,” Exp. Fluids 23 (1), 20-28 (1997).
    doi 10.1007/s003480050082.
  14. J. Chen and J. Katz, “Elimination of Peak-Locking Error in PIV Analysis Using the Correlation Mapping Method,” Meas. Sci. Technol. 16 (8), 1605-1618 (2005).
    doi 10.1088/0957-0233/16/8/010.
  15. J. Westerweel and F. Scarano, “Universal Outlier Detection for PIV Data,” Exp. Fluids 39 (6), 1096-1100 (2005).
    doi 10.1007/s00348-005-0016-6.
  16. S. Tiwari and J. Kuhnert, Grid Free Method for Solving the Poisson Equation , Volume 25 of Berichte (Fraunhofer Institut Techno- und Wirtschaftsmathematik, Kaiserslautern, 2001).
  17. M. Stanislas, K. Okamoto, C. J. Kähler, et al., “Main Results of the Third International PIV Challenge,” Exp. Fluids 45 (1), 27-71 (2008).
    doi 10.1007/s00348-008-0462-z.
  18. B. Lecordier and J. Westerweel, “The EUROPIV Synthetic Image Generator (S.I.G.),” in Particle Image Velocimetry: Recent Improvements (Springer, Berlin, 2004), pp. 145-161.
    doi 10.1007/978-3-642-18795-7_11.
  19. M. Frigo and S. G. Johnson, “The Design and Implementation of FFTW3,” Proc. IEEE 93 (2), 216-231 (2005).
    doi 10.1109/JPROC.2004.840301.



How to Cite

Зарипов Д. И., Токарев М. П., Лукьянов А. А., Маркович Д. М. Grid-Free Planar Method of Particle Image Velocimetry // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2022. 23. 328-338. doi 10.26089/NumMet.v23r420



Methods and algorithms of computational mathematics and their applications