Modified <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> D Laplacian for smooth pressure reconstruction based

Abstract In this work, a modified Laplacian pressure Poisson reconstruction technique has been studied using experimental velocimetry data, after the theoretical investigation in the companion work (Zhang et al 2024 Meas. Sci. Technol. 35 095302). The modified solver adds a temporal diffusion term to the canonical Laplacian operator to mitigate the high frequency noise in the pressure fields reconstructed from time-resolved velocimetry data. The current work uses time-resolved tomographic particle image velocimetry (PIV) measurements of an impinging synthetic jet with a commercial version of the modified Laplacian solver, known as a 4D solver, to reconstruct the instantaneous pressure fields. While the reconstructed pressure fields are smooth in time, they often display a non-physical temporal drift. Using Fourier spectral decomposition of the reconstructed pressure field and the source term of the pressure Poisson equation, we demonstrate that the smoothing behavior is the result of a low-pass filtering effect during the inversion of the modified Laplacian. Both the weighting factor of the temporal diffusion term and the space-time splitting of the time-series data affect the filtering behavior, and therefore, the smoothing effect of this modified 4D Laplacian pressure Poisson solver. Along with the weighting factor and the number of space-time blocks, the temporal drift is also affected by flow oscillation and temporal resolution of the experimental data. This study shows that, with a proper selection of different parameters, it is possible to remove the non-physical high-frequency noise from the pressure fields and limit the temporal drift. Last, we demonstrate that a physical measurement may be used to tune the parameters of this modified Laplacian based solver.