Computing the finite time Lyapunov exponent for flows with uncertainties

JOURNAL OF COMPUTATIONAL PHYSICS

卷:425

Article

You, Guoqiao¹  Leung, Shingyu² 

[1] Nanjing Audit Univ, Sch Stat & Math, Nanjing 211815, Peoples R China

[2] Hong Kong Univ Sci & Technol, Dept Math, Clear Water Bay, Hong Kong, Peoples R China

关键词: Finite time Lyapunov exponent;    Flow visualization;    Uncertainty;    Dynamical systems;    Numerical methods for PDEs;   

DOI  :  10.1016/j.jcp.2020.109905

来源: Elsevier

【 摘 要 】

We propose an Eulerian approach to compute the expected finite time Lyapunov exponent (FTLE) of uncertain flow fields. The definition extends the usual FTLE for deterministic dynamical systems. Instead of performing Monte Carlo simulations as in typical Lagrangian computations, our approach associates each initial flow particle with a probability density function (PDF) which satisfies an advection-diffusion equation known as the Fokker-Planck (FP) equation. Numerically, we incorporate Strang's splitting scheme so that we can obtain a second-order accurate solution to the equation. To further improve the computational efficiency, we develop an adaptive approach to concentrate the computation of the FTLE near the ridge, where the so-called Lagrangian coherent structure (LCS) might exist. We will apply our proposed algorithm to several test examples including a real-life dataset to demonstrate the performance of the method. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free