Berkeley Fluids Seminar

University of California, Berkeley

Bring your lunch(have room for some seminar snacks) and enjoy learning about fluids!

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What: Fluids

When: TBD, 12 noon

Where: 3110, Etcheverry Hall

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Eric Ibarra

aquamanbell AT berkeley.edu


Haris Sheikh

harissheikh AT berkeley.edu


Spectral Representation and Approximation of Solenoidal Fields

Monday, April 1, 2019

12:00-13:00, 3110 Etcheverry Hall

Siavash Ameli

(Mechanical Engineering)



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.



Bio: Siavash Ameli is PhD candidate at department of Mechanical engineering, UC Berkeley. He works with Prof. Shawn Shadden and his areas of research include dynamical systems, stochastic modeling and differential geometry.





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Acknowledgments

Prof. Eliot Quataert on behalf of The Theoretical Astrophysics Center and the Astronomy Department (UC Berkeley)

Prof. Philip S. Marcus on behalf of the Mechanical Engineering Department (UC Berkeley)

Prof. Michael Manga (Earth and Planetary Science, UC Berkeley)

Prof. Evan Variano (Civil and Environmental Engineering, UC Berkeley)


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