ROBUST GRADIENT ESTIMATION USING RADIAL BASIS FUNCTIONS

Utilization of Radial Basis Functions (RBFs) for gradient estimation is tested over various noisy flow fields. A novel mathematical formulation which minimizes the energy functional associated with the analytical surface fit for Gaussian (GA) and Generalized Multiquadratic (GMQ) RBFs is presented. Error analysis of the wall gradient estimation was performed at various resolutions, interpolation grid sizes, and noise levels in synthetically generated Poiseuille and Womersley flow fields for RBFs along with standard finite difference schemes. To test the effectiveness of the methods with DPIV (Digital Particle Image Velocimetry) data, the methods were compared using the velocities obtained by processing images generated from DNS data of an open turbulent channel. Random, bias and total error were computed in all cases. In the absence of noise all tested methods perform well, with error contained under 10% at all resolutions. In the presence of noise the RBFs perform robustly with a total error that can be contained under 10-15% even with 10% noise using various interpolation grid sizes, For turbulent flow data, although the total error is approximately 5% for finite difference schemes in the absence of noise, the error can go as high as 150% in the presence of as little as 1% noise. With DPIV processed data the error is 25-40% for TPS and MQ methods optimization of the fitting parameters that minimize the energy functional associated with the analytical surface using RBFs results in robust gradient estimators are obtained that are applicable to steady, unsteady and turbulent flow fields.