TY - JOUR
T1 - Eulerian Algorithms for Computing the Forward Finite Time Lyapunov Exponent Without Finite Difference upon the Flow Map
AU - You , Guoqiao
AU - Xue , Changfeng
AU - Deng , Shaozhong
JO - Communications in Computational Physics
VL - 5
SP - 1467
EP - 1488
PY - 2022
DA - 2022/05
SN - 31
DO - http://doi.org/10.4208/cicp.OA-2021-0193
UR - https://global-sci.org/intro/article_detail/cicp/20511.html
KW - Finite time Lyapunov exponent, flow map, flow visualization, dynamical system.
AB - <p style="text-align: justify;">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.</p>