Pressure Reconstruction from Noisy Measurements of Pressure Gradient by Gaussian Process Regression in Isotropic Turbulence

An accurate estimation of the pressure fields is of vital importance in various fluid dynamics applications. However, non-intrusive, direct pressure measurement techniques with high resolution are often very challenging. Consequently, many numerical tools have been established to reconstruct pressure fields from material acceleration obtained by Particle Image Velocimetry (PIV), such as the state-of-art Omni-directional Integration(ODI) method. This study introduces the framework of the Gaussian Process Regression(GPR) method to reconstruct the pressure field from material acceleration embedded with measurement noise. Similar to the testing method used in Liu and Moreto (2020), pressure gradient fields from Johns Hopkins Turbulent database are superimposed with 1000 statistically independent homogeneous error distributions to conduct a comparison of real and reconstructed pressure fields by ODI and GPR methods. The preliminary result demonstrates that GPR method with radial basis kernel function enables a versatile application in random and sparse observations with the same accuracy as the ODI method. Furthermore, this study provides an extended mathematical explanation of noise reduction by comparing different variance kernels of the Gaussian Process.