title: Integrated computation of finite-time Lyapunov exponent fields during direct numerical simulation of unsteady flows.
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, J. Comput. Phys. 230, 3500-3524 (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, 017503 (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.
authors.affiliation: School of Mechanical, Industrial and Manufacturing Engineering, Oregon State University, 204 Rogers Hall, Corvallis, Oregon 97331, USA. finnj@engr.oregonstate.edu
authors.forename: Justin
authors.initials: J
authors.lastname: Finn
authors.forename: Sourabh V
authors.initials: SV
authors.lastname: Apte
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005246:Feedback; D008962:Models, Theoretical; D009038:Motion; D009716:Numerical Analysis, Computer-Assisted; D012212:Rheology; D013997:Time Factors; D014783:Viscosity