Skip to main content
SpringerLink
Log in

A variational filtration and interpolation technique for PIV employing fluid dynamical constraints

  • Research Article
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

A variational method for post-processing of the velocity fields obtained by particle image velocimetry (PIV) is described. This method allows one to effectively reconstruct the flow field in the areas of the domain where the spurious vectors were discarded either by other filters or manually. If the spurious vectors cannot be removed, they are smoothed in with the surrounding field so that their effect is significantly reduced. The method is based on the application of dynamical constraints such as continuity, smoothness and matching to the original data. The results of the application of the developed algorithm to the velocity fields obtained by PIV in laboratory experiments with quasi-two-dimensional vortex dipoles are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Adrian RJ (1991) Particle-imaging techniques for experimental fluid mechanics. Annu Rev Fluid Mech 23:261–304

    Article  Google Scholar 

  • Afanasyev YD, Kostianoy AG, Zatsepin AG, Poulain PM (2002) Analysis of velocity field in the eastern Black Sea from satellite data during the “Black Sea’99” Experiment. J Geophys Res Oceans 107 (10.1029/2000JC000578)

  • Amodei L (1991) A vector spline approximation. J Approx Theory 67:51–79

    Article  MATH  MathSciNet  Google Scholar 

  • Batchelor GK (1967) An introduction to fluid dynamics. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Brucker Ch (1995) Digital-particle-image-velocimetry (DPIV) in a scanning light-sheet: 3-D starting flow around a short cylinder. Exp Fluids 19:255–263

    Article  Google Scholar 

  • Fincham A (2003) 3 component, volumetric, time-resolved scanning correlation imaging velocimetry. Proceedings of the Fifth International Symposium on Particle Image Velocimetry, Busan, Korea, pp 2–16

  • Fincham A, Spedding G (1997) Low cost, high resolution DPIV for measurement of turbulent fluid flow. Exp Fluids 23:449–462

    Article  Google Scholar 

  • Gilbert JC, Lemarechal C (1989) Some numerical experiments with variable storage quasi-Newton algorithms. Math Program 45:407–455

    Article  MATH  MathSciNet  Google Scholar 

  • Memin E, Perez P (2002) Hierarchical estimation and segmentation of dense motion fields. Int J Comput Vision 46:129–155

    Article  MATH  Google Scholar 

  • Panteleev GG, Maximenko NA, deYoung B, Reiss C, Yamagata T (2002) Variational interpolation of circulation with nonlinear, advective smoothing. J Atmos Ocean Technol 19(9):1442–1450

    Article  Google Scholar 

  • Paret J, Marteau D, Paireau O, Tabeling P (1997) Are flows electromagnetically forced in thin stratified layers two dimensional. Phys Fluids 9:3102–3106

    Article  MATH  MathSciNet  Google Scholar 

  • Pawlak G, Armi L (1998) Vortex dynamics in a spatially accelerating shear layer. J Fluid Mech 376:1–30

    Article  MathSciNet  MATH  Google Scholar 

  • Ramamurthy MK, Navon IM (1992) The conjugate-gradient variational analysis and initialization method: an application to MONEX SOP-2 data. Mon Weather Rev 120:2360–2377

    Article  Google Scholar 

  • Rockwell D, Magness C, Towfighi J, Akin O, Corcoran T (1993) High image-density particle image velocimetry using laser scanning techniques. Exp Fluids 14:181–192

    Article  Google Scholar 

  • Shapiro R (1970) Smoothing, filtering, and boundary effects. Rev Geophys Space Phys 8:359–387

    Google Scholar 

  • Shapiro R (1975) Linear filtering. Math Comput 29:1094–1097

    Article  MATH  Google Scholar 

  • Thacker WC (1988) Fitting models to inadequate data by enforcing spatial and temporal smoothing. J Geophys Res 93:10655–10665

    Google Scholar 

  • Utami T, Ueno T (1984) Visualization and picture processing of turbulent flow. Exp Fluids 2:25–32

    Article  Google Scholar 

  • Voropayev SI, Afanasyev YD (1994) Vortex structures in a stratified fluid. Chapman & Hall, London

    MATH  Google Scholar 

  • Voropayev SI, Afanasyev YD, Filippov IA (1991) Horizontal jets and vortex dipoles in a stratified fluid. J Fluid Mech 227:543

    Article  Google Scholar 

  • Wells J, Afanasyev YD (2004) Decaying quasi-two-dimensional turbulence in a rectangular container: laboratory experiments. Geophys Astrophys Fluid Dyn 98:1–20

    Article  MathSciNet  Google Scholar 

  • Westerweel J (1994) Efficient detection of spurious vectors in particle image velocimetry data. Exp Fluids 16:236–247

    Article  Google Scholar 

Download references

Acknowledgements

The research reported in this paper was supported by the Natural Sciences and Engineering Research Council of Canada under grants 300805-04 and 227192-04.

Author information

Authors and Affiliations

  1. Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John‘s, NL, Canada

    Y. D. Afanasyev & E. K. Demirov

Authors
  1. Y. D. Afanasyev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. K. Demirov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Y. D. Afanasyev.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Afanasyev, Y.D., Demirov, E.K. A variational filtration and interpolation technique for PIV employing fluid dynamical constraints. Exp Fluids 39, 828–835 (2005). https://doi.org/10.1007/s00348-005-0017-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00348-005-0017-5

Keywords

Search

Navigation