Attraction-Based Computation of Hyperbolic Lagrangian Coherent Structures

TL;DR

This paper introduces a robust, low-cost method for computing hyperbolic Lagrangian Coherent Structures at arbitrary times by advecting only attracting material surfaces, improving accuracy and stability over previous techniques.

Contribution

The authors develop a novel approach that allows for stable and accurate computation of hyperbolic LCS at any time by focusing solely on attracting surfaces, overcoming previous numerical instability issues.

Findings

Method successfully tracks LCS at arbitrary times

Approach is computationally efficient and robust

Validated on simple and turbulent flow data

Abstract

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.