Eulerian Algorithms for Computing the Forward Finite Time Lyapunov Exponent Without Finite Difference upon the Flow Map (Communications in Computational Physics, 2022)
In this paper, effective Eulerian algorithms are introduced for the computation of the forward finite time Lyapunov exponent (FTLE) of smooth flow fields. Theadvantages of the proposed algorithms mainly manifest in two aspects. First, previousEulerian approaches for computing the FTLE field are improved so that the Jacobianof the flow map can be obtained by directly solving a corresponding system of partialdifferential equations, rather than by implementing certain finite difference upon theflow map, which can significantly improve the accuracy of the numerical solution especially near the FTLE ridges. Second, in the proposed algorithms, all computationsare done on the fly, that is, all required partial differential equations are solved forward in time, which is practically more natural. The new algorithms still maintain theoptimal computational complexity as well as the second order accuracy. Numericalexamples demonstrate the effectiveness of the proposed algorithms.
Keywords: Finite time Lyapunov exponent; flow map; flow visualization; dynamical system.