Fast computation of finite-time Lyapunov exponent fields for unsteady flows

This paper presents new efficient methods for computing finite-time Lyapunov exponent (FTLE) fields in unsteady flows. The methods approximate the particle flow map, eliminating redundant particle integrations in neighboring flow map calculations. Two classes of flow map approximations are investigated based on composition of intermediate flow maps; unidirectional approximation constructs a time-T map by composing a number of smaller time-h maps, while bidirectional approximation constructs a flow map by composing both positive- and negative-time maps. The unidirectional method is shown to be fast and accurate, although it is memory intensive. The bidirectional method is also fast and uses significantly less memory; however, it is prone to error which is large in regions where the opposite-time FTLE field is large, rendering it unusable. The algorithms are implemented and compared on three example fluid flows: a double gyre, a low Reynolds number pitching flat plate, and an unsteady ABC flow.