Optical Flow Velocimetry using a Quasi-Optimal Basis with Implicit Regularization
Gauresh Raj Jassal, Julia A. Dobrosotskaya, Bryan Eric Schmidt · AIAA AVIATION 2022 Forum · 2022
View Video Presentation: https://doi.org/10.2514/6.2022-3336.vid A set of quasi-optimal bases of orthonormal functions to represent fluid flow fields are formed using the singular value decomposition of a diverse set of direct numerical simulations (DNS) of various turbulent flows. It is found that the bases are capable of sparsely representing a wide variety of fluid flow fields with minimal accuracy loss, and hence can be effectively used to solve the ill-posed optical flow problem to perform optical flow velocimetry (OFV), by reducing the dimensionality of the problem to resolve the ill-posedness. A novel OFV method is developed using the new quasi-optimal basis with implicit regularization. The bases can impose implicit regularization on the solution via truncation of coefficients, which acts as a physics-informed smoothing. The effect of the user defined parameters, including the patch size, on the bases themselves and on the resulting OFV solutions, and it is found that at small enough patch size, the quality of the reconstructions with the quasi-optimal bases are dataset independent, indicating universality in the flow structures at small scales.