American Institute of Mathematical Sciences

January  2015, 2(1): 83-93. doi: 10.3934/jcd.2015.2.83

Attraction-based computation of hyperbolic Lagrangian coherent structures

 1 ETH Zürich, Institute of Mechanical Systems, Leonhardstrasse 21, 8092 Zürich, Switzerland, Switzerland 2 ETH Zürich, Institute of Mechanical Systems, Rämistrasse 101, 8092 Zürich, Switzerland

Received  May 2014 Revised  October 2014 Published  August 2015

Recent advances enable the simultaneous computation of both attracting and repelling families of Lagrangian Coherent Structures (LCS) at the same initial or final time of interest. Obtaining LCS positions at intermediate times, however, has been problematic, because either the repelling or the attracting family is unstable with respect to numerical advection in a given time direction. Here we develop a new approach to compute arbitrary positions of hyperbolic LCS in a numerically robust fashion. Our approach only involves the advection of attracting material surfaces, thereby providing accurate LCS tracking at low computational cost. We illustrate the advantages of this approach on a simple model and on a turbulent velocity data set.
Citation: Daniel Karrasch, Mohammad Farazmand, George Haller. Attraction-based computation of hyperbolic Lagrangian coherent structures. Journal of Computational Dynamics, 2015, 2 (1) : 83-93. doi: 10.3934/jcd.2015.2.83
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