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Computation of Forward-Time Finite-Time Lyapunov Exponents Using Discontinuous-Galerkin Spectral Element Methods

[+] Author Affiliations
Daniel A. Nelson, Gustaaf B. Jacobs

San Diego State University, San Diego, CA

Paper No. IMECE2013-64997, pp. V015T16A015; 10 pages
doi:10.1115/IMECE2013-64997
From:
  • ASME 2013 International Mechanical Engineering Congress and Exposition
  • Volume 15: Safety, Reliability and Risk; Virtual Podium (Posters)
  • San Diego, California, USA, November 15–21, 2013
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5644-4
  • Copyright © 2013 by ASME

abstract

We present an algorithm for computing forward-time finite-time Lyapunov exponents (FTLEs) using discontinuous-Galerkin (DG) operators. Passive fluid tracers are initialized at Gauss-Lobatto quadrature nodes and advected concurrently with direct numerical simulation (DNS) using DG spectral element methods. The flow map is approximated by a high-order polynomial and the deformation gradient tensor is then determined by the spectral derivative. Since DG operators are used to compute the deformation gradient, the algorithm is high-order accurate and is consistent with the DG methods used to compute the fluid solution. The method is validated with a benchmark of a periodic gyre, a vortex advected in uniform flow and the flow around a square cylinder. An exact equation for the FTLE of the advected vortex is derived.

Copyright © 2013 by ASME

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