A ridge tracking algorithm for the computation and extraction of Lagrangian coherent structures ͑LCS͒ is developed. This algorithm takes advantage of the spatial coherence of LCS by tracking the ridges which form LCS to avoid unnecessary computations away from the ridges. We also make use of the temporal coherence of LCS by approximating the time dependent motion of the LCS with passive tracer particles. To justify this approximation, we provide an estimate of the difference between the motion of the LCS and that of tracer particles which begin on the LCS. In addition to the speedup in computational time, the ridge tracking algorithm uses less memory and results in smaller output files than the standard LCS algorithm. Finally, we apply our ridge tracking algorithm to two test cases, an analytically defined double gyre as well as the more complicated example of the numerical simulation of a swimming jellyfish. In our test cases, we find up to a 35 times speedup when compared with the standard LCS algorithm. © 2010 American Institute of Physics. ͓doi:10.1063/1.3270049͔ One of the biggest problems in fluid dynamics is analyzing data. As computational fluid dynamics (CFD) codes become more sophisticated and produce larger and more complex results for increasingly complicated flows, extracting meaningful results from the resulting fluid velocities becomes ever more challenging. Over the past several years, Lagrangian coherent structures (LCS) have emerged as an excellent way to visualize and analyze such flow fields. These structures represent barriers to transport and can be used to identify exact vortex boundaries, providing an unambiguous visual characterization of the flow field. They may also be used to extract quantitative measures of mixing and transport in the flow. However, the Lagrangian nature of LCS makes their computation extremely expensive, sometimes prohibitively so. Computations in two dimensions are extremely expensive and in three dimensions the problem is even worse. In this paper we present an algorithm which takes advantage of the temporal and spatial coherences of LCS to greatly speed computations. This algorithm tracks the ridges in the finite time Lyapunov exponent (FTLE) field at each time step, then approximates the location of the ridges at the next time step by advecting the LCS forward with the flow. A simple error estimate shows that the difference between the advected LCS and the actual LCS is typically very small. In the end, our algorithm proves to be very useful for extracting the major LCS present in a flow field and gives a speedup of up to 35 times.
Lipinski and Mohseni REF present a ridge tracking algorithm for FTLE fields that uses both temporal and spatial coherency of LCS, and give an error estimator for the difference between the advected ridge the and actual LCS.
A ridge tracking algorithm and error estimate for efficient computation of Lagrangian coherent structures
Chaos
Chaos
Mathematics Medicine