Solenoidal filtering of volumetric velocity measurements using Gaussian process regression

Optimization of planar PIV-based pressure estimates in laminar and turbulent wakes

“…Similar to the approach employed in previous studies (e.g., Charonko et al 2010;Azijli and Dwight 2015), Gaussian random noise was added to the synthetic velocity fields proportional to the magnitude of each velocity component (ũ = u(1 + u )) to simulate measurement noise. The noise level ( u ) was varied between 0 and 2.5% in 0.25% increments to capture the initial error response characteristics, which for a given methodology have been shown to extrapolate to higher noise levels (de Kat and van Oudheusden 2012; Charonko et al 2010).…”

A posteriori uncertainty quantification of PIV-based pressure data

“…From top to bottom: without applying the prior knowledge of divergencefree velocity fields through the solenoidal filter and using the Eulerian approach; without the prior knowledge using the Lagrangian approach; including the solenoidal prior and using the Eulerian approach; including the solenoidal prior and using the Lagrangian approach. From the figure, we can already deduce the observations made by Violato et al (2011), namely that the Lagrangian approach results in more accurate pressure reconstruction than the Eulerian approach, and the observations made by Azijli and Dwight (2015) that using the solenoidal prior improves the pressure reconstruction.…”

“…that constrains the velocity components according to mass conservation (the divergence-free or solenoidal constraint) (Azijli and Dwight 2015). The details can be found in these works.…”

“…They can either be specified a priori or through a maximum likelihood optimization. Azijli and Dwight (2015) followed the a priori approach. This was possible because the PIV data had sufficient spatial resolution.…”

“…10) and its uncertainty (Eq. 12), respectively; (2) realizing the flow is incompressible, we enforce the divergence-free constraint by applying a solenoidal filter (Azijli and Dwight 2015). The solenoidal filter is linear; therefore, the posterior distribution will remain Gaussian distributed (Fig.…”