An improved Eulerian approach for the finite time Lyapunov exponent
Proposed is a new Eulerian numerical approach to compute the Jacobian of flow maps in continuous dynamical systems and, subsequently, the so-called finite time Lyapunov exponent (FTLE) for Lagrangian coherent structure extraction. The original approach computes the flow map and then numerically determines the Jacobian of the map using finite differences. The new algorithm improves the original Eulerian formulation so that at first partial differential equations for each component of the Jacobian are obtained, and then these equations are solved to obtain the required Jacobian. For periodic dynamical systems, based on the time doubling technique developed for computing the longtime flow map, a new efficient iterative method is also proposed to compute the Jacobian of the longtime flow map. Numerical examples demonstrate that the new proposed approach is more accurate than the original one in computing the Jacobian and thus the FTLE field, especially near the FTLE ridges.
scientific article; zbMATH DE number 6945480
scientific article