Eulerian Algorithms for Computing the Forward Finite Time Lyapunov Exponent Without Finite Difference upon the Flow Map
Year: 2022
Author: Guoqiao You, Changfeng Xue, Shaozhong Deng
Communications in Computational Physics, Vol. 31 (2022), Iss. 5 : pp. 1467–1488
Abstract
In this paper, effective Eulerian algorithms are introduced for the computation of the forward finite time Lyapunov exponent (FTLE) of smooth flow fields. The advantages of the proposed algorithms mainly manifest in two aspects. First, previous Eulerian approaches for computing the FTLE field are improved so that the Jacobian of the flow map can be obtained by directly solving a corresponding system of partial differential equations, rather than by implementing certain finite difference upon the flow map, which can significantly improve the accuracy of the numerical solution especially near the FTLE ridges. Second, in the proposed algorithms, all computations are 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 the optimal computational complexity as well as the second order accuracy. Numerical examples demonstrate the effectiveness of the proposed algorithms.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2021-0193
Communications in Computational Physics, Vol. 31 (2022), Iss. 5 : pp. 1467–1488
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Finite time Lyapunov exponent flow map flow visualization dynamical system.