Exploration of Tikhonov regularization for the fusion of experimental data and computational fluid dynamics
Meade, Andrew J., Jr.
Master of Science
A method is developed to fuse Computational Fluid Dynamics (CFD) simulations and experimental data through the use of Tikhonov regularization. Inviscid-Viscous Interaction and Thin-Layer Navier-Stokes Equation models are used to provide CFD solutions for the flow past NACA 0012 and RAE 2822 airfoils, respectively. The velocity profile within the boundary layer and the pressure coefficient on the surface of the airfoil are merged with the corresponding experimental data. A finite element approach is applied to accomplish the numerical solution of the Tikhonov regularization method. By using over- or under-relaxation technique, relatively few iterations are needed to achieve the convergence of the fusion method. The results demonstrate that a-priori CFD solutions of low fidelity can be improved by the experimental data with less computational cost compared with more sophisticated CFD models. Alternatively, the sparse and scattered experimental data are efficiently processed by utilizing CFD models as regularization. The limitations of the Tikhonov regularization method have been examined. The result shows that the fusion method has significant advantages over a nonlinear least-square polynomial approach for interpolating and extrapolating experimental data.