Methodologies to acquire three-dimensional velocity fields are becoming increasingly available, generating large datasets of steady state and transient flows of engineering and/or biomedical interest. This paper presents a novel linear filter for three-dimensional velocity acquisitions, which eliminates the spurious velocity divergence due to measurement errors. The noise reduction properties of the associated linear operator are discussed together with the treatment of boundary conditions and efficient handling of large measurement datasets. Examples show the application of the technique to real velocity fields acquired through Magnetic Resonance Velocimetry as well as Particle Image Velocimetry. The effectiveness of the filter is demonstrated by application to synthetic velocity fields obtained from analytical solutions and computations. The filter eliminates about half of the noise, without artificial smoothing of the original data, and conserves localized flow features.
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We are indebted to Dr. Bernd Wieneke for suggesting the IDA method as a reference approach and providing insights on its denoising properties. We wish to thank Julia Ling at Stanford University and Riccardo Rossi at Università di Bologna for providing the RANS simulation of the jet in crossflow and direct simulation of the flow around the wall-mounted cube, respectively. The first author would like to thank Paul Constantine and Carlos Sing-Long at Stanford University for useful discussion and comments on numerical evaluation of the noise reduction properties of the linear filter operator. PIV 3D measurements of the flow around a swimming jellyfish were kindly provided by Brad Gemmell, Marine Biological Laboratory, Woods Hole, MA. The authors would also like to thank Ivan Bermejo-Moreno for helpful suggestions and comments in an earlier version of this paper. Finally, we would like to thank the anonymous Reviewers for providing useful comments and suggesting references that improved significantly the comparison with other approaches in the literature. G.I.'s and D.S.'s work is supported under Subcontract No. B597952 with Lawrence Livermore National Security under Prime Contract No. DE-AC52-07NA27344 from the Department of Energy National Nuclear Security Administration for the Management and Operation of the Lawrence Livermore National Laboratory . F.C.'s work is supported by a grant from the Honeywell Corporation .
- Divergence-free filtering
- Magnetic resonance velocimetry
- Matching pursuit
- Particle image velocimetry
- Velocity field de-noising