Spectral Representation and Approximation of Solenoidal Fields: Fluids Seminar
Seminar | April 1 | 12-1 p.m. | 3110 Etcheverry Hall
Siavash Ameli, Ph.D. Candidate, Department of Mechanical Engineering, University of California, Berkeley
Abstract: Wide range of fluid flow applications are incompressible. Noise in flow measurements is the main source that violates the divergence free condition for such flows. Variety of approaches has been proposed to filter noise and reconstruct data. Proper Orthogonal Decomposition, Dynamics Mode Decomposition, radial basis functions and smoothing kernels, spectral filtering by Fourier representation and wavelet transforms are few examples. Despite the rich capabilities of these approaches, they do not address the divergence free constraint of the incompressible fluid flow. In this talk, the spectral representation of multi-dimensional vector fields are presented by means of orthogonal family of solenoidal fields. The set of eigenfunctions form a complete basis that span the divergent-free Sobolev space. The spectral representation of the fluid flow is obtained by the Galerkin projection of the flow to these eigenmodes that satisfy the flow boundary condition. The convergence rate and error bound of approximation are presented. We discuss the optimality of the set of eigenfunctions, and their application in supervised learning of incompressible fluid flows. We demonstrate examples of filtering and reconstruction of incomplete flow measurements with Bayesian inference framework.
Biography: Siavash Ameli is a Ph.D. candidate in the Department of Mechanical engineering at UC Berkeley. He works with Professor Shawn Shadden, and his areas of research include dynamical systems, stochastic modeling and differential geometry.