Weighted divergence correction scheme and its fast implementation

  • ChengYue Wang
  • Qi Gao
  • RunJie Wei
  • Tian Li
  • JinJun Wang
Research Article


Forcing the experimental volumetric velocity fields to satisfy mass conversation principles has been proved beneficial for improving the quality of measured data. A number of correction methods including the divergence correction scheme (DCS) have been proposed to remove divergence errors from measurement velocity fields. For tomographic particle image velocimetry (TPIV) data, the measurement uncertainty for the velocity component along the light thickness direction is typically much larger than for the other two components. Such biased measurement errors would weaken the performance of traditional correction methods. The paper proposes a variant for the existing DCS by adding weighting coefficients to the three velocity components, named as the weighting DCS (WDCS). The generalized cross validation (GCV) method is employed to choose the suitable weighting coefficients. A fast algorithm for DCS or WDCS is developed, making the correction process significantly low-cost to implement. WDCS has strong advantages when correcting velocity components with biased noise levels. Numerical tests validate the accuracy and efficiency of the fast algorithm, the effectiveness of GCV method, and the advantages of WDCS. Lastly, DCS and WDCS are employed to process experimental velocity fields from the TPIV measurement of a turbulent boundary layer. This shows that WDCS achieves a better performance than DCS in improving some flow statistics.


Direct Numerical Simulation Weighting Coefficient Correlate Noise Noise Strength Generalize Cross Validation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work is supported by the National Natural Science Foundation of China (11327202, 11472030, 11490552) and the Fundamental Research Funds for Central Universities (YWF-16-JCTD-A-05).

Supplementary material

348_2017_2307_MOESM1_ESM.txt (2 kb)
Appendix (TXT 2.22 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Key Laboratory of Fluid Mechanics, Ministry of EducationBeijing University of Aeronautics and AstronauticsBeijingChina
  2. 2.Shenyang Aircraft Design and Research InstituteShengyangChina
  3. 3.MicroVec., IncBeijingChina

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