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Integrated computation of finite-time Lyapunov exponent fields during direct numerical simulation of unsteady flows

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Abstract
  • The computation of Lagrangian coherent structures typically involves post-processing of experimentally or numerically obtained fluid velocity fields to obtain the largest finite-time Lyapunov exponent (FTLE) field. However, this procedure can be tedious for large-scale complex flows of general interest. In this work, an alternative approach involving computation of the FTLE on-the-fly during direct numerical simulation of the full three dimensional Navier-Stokes equations is developed. The implementation relies on Lagrangian particle tracking to compose forward time flow maps, and an Eulerian treatment of the backward time flow map [S. Leung, Journal of Computational Physics 230, 2011] coupled with a semi-Lagrangian advection scheme. The flow maps are accurately constructed from a sequence of smaller sub-steps stored on disk [S. Brunton and C. Rowley, Chaos 20, 2010], resulting in low CPU and memory requirements to compute evolving FTLE fields. Several examples are presented to demonstrate the capability and parallel scalability of the approach for a variety of two and three dimensional flows.
  • Keywords: Largest finite-time Lyapunov exponent (FTLE), Lagrangian coherent structures
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  • Finn, J., & Apte, S. V. (2013). Integrated computation of finite-time Lyapunov exponent fields during direct numerical simulation of unsteady flows. Chaos (Woodbury, N.Y.), 23(1), 013145. doi:10.1063/1.4795749
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  • 23
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  • 1
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  • This work was supported by the National Science Foundation (Project #0933857: Inertial Effects in Flow Through Porous Media). We gratefully acknowledge the grants for computing time on the Lonestar supercomputer at the Texas Advanced Computing Center (TACC).
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