Time Line Cell Tracking for the Approximation of Lagrangian Coherent Structures with Subgrid Accuracy

• Published in: Computer graphics forum 2014-02, Vol.33 (1), p.222-234
• Main Authors: Kuhn, A., Engelke, W., Rössl, C., Hadwiger, M., Theisel, H.
• Format: Article
• Language: English
• Subjects: Approximation; finite-time Lyapunov exponents (FTLE); finite-time Lyapunov exponents (FTLEs); flow field visualization; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-time-dependent vector fields; Lagrangian Coherent Structures (LCS); Lagrangian Coherent Structures (LCSs); material surfaces; time lines; time-dependent vector fields
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12269

Lagrangian coherent structures (LCSs) have become a widespread and powerful method to describe dynamic motion patterns in time‐dependent flow fields. The standard way to extract LCS is to compute height ridges in the finite‐time Lyapunov exponent field. In this work, we present an alternative method to approximate Lagrangian features for 2D unsteady flow fields that achieve subgrid accuracy without additional particle sampling. We obtain this by a geometric reconstruction of the flow map using additional material constraints for the available samples. In comparison to the standard method, this allows for a more accurate global approximation of LCS on sparse grids and for long integration intervals. The proposed algorithm works directly on a set of given particle trajectories and without additional flow map derivatives. We demonstrate its application for a set of computational fluid dynamic examples, as well as trajectories acquired by Lagrangian methods, and discuss its benefits and limitations. Lagrangian Coherent Structures (LCS) have become a widespread and powerful method to describe dynamic motion patterns in time‐dependent flow fields. The standard way to extract LCS is to compute height ridges in the Finite Time Lyapunov Exponent (FTLE) field. In this work, we present an alternative method to approximate Lagrangian features for 2D unsteady flow fields that achieves subgrid accuracy without additional particle sampling. We obtain this by a geometric reconstruction of the flow map using additional material constraints for the available samples. The illustration shows four approximations of LCS at different time steps in subgrid accuracy computed from a triangular grid containing 60 times 120 sample points for a heated cylinder simulation.