A matching pursuit approach to solenoidal filtering of three-dimensional velocity measurements

Abstract

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. Examples show the application of the technique to real velocity fields acquired through volumetric 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.

Divergence-Free Wavelet Frames

“…Since our method is redundant (redundancy factor 3), we also include the cycle-spun version of the bi-orthogonal divergence-free wavelets (redundancy factor 8). As a baseline method, Leray projection, which is implemented as a Fourier domain filtering using (6), is incorporated in the comparisons.…”

“…Volumetric particle image velocimetry (vPIV) techniques are also capable of measuring three-dimensional velocity fields. Similar ideas have recently been applied to vPIV data by removing spurious divergence through a redundant atomic signal decomposition [6].…”

Solenoidal filtering of volumetric velocity measurements using Gaussian process regression

“…Another choice of basis is described in the work by Schiavazzi et al (2014), who introduced a method, referred to in the following as solenoidal waveform reconstruction (SWR), where vortices around the edges of the measurement grid are placed, ensuring a solenoidal velocity field on a finite-volume level. It works as follows: After creating a Voronoi tessellation associated with the measurement grid, the measured velocities are converted to face fluxes.…”

“…The first does not enforce the divergencefree constraint, and works through a convolution of the data using a 3 × 3 smoothing kernel with equal weights (BOX 3×3 ), a simple yet widely used approach to dealing with noisy data (Raffel et al 1998). The two solenoidal filters we compare with are DCS (de Silva et al 2013) and SWR (Schiavazzi et al 2014). A detailed description of the specific implementations of these two filters in the present paper can be found in the Appendices 1 and 2.…”

“…Solenoidal waveform reconstruction (SWR), as proposed by Schiavazzi et al (2014), works by first defining a Voronoi tessellation of the measurement grid. Then, the observed velocities u PIV are converted to face fluxes g. Vortices with unknown strengths α α α are defined around all edges of the grid (in 2D, vortices are defined around nodes).…”