FAST IDENTIFICATION OF THE HYPERBOLIC LAGRANGIAN COHERENT STRUCTURES IN TWO-DIMENSIONAL FLOWS BASED ON THE EULERIAN-TYPE ALGORITHMS

Abstract

<abstract> Based on the so-called mixing-based partition, we propose an efficient Eulerian algorithm to identify the hyperbolic Lagrangian coherent structure (LCS) of any given two-dimensional (2D) flow fields, which is framework independent. To extract the required LCS, the proposed algorithm only needs to solve one single partial differential equation. Moreover, data is only required at mesh points in the implementation of the proposed algorithm. In contrast, traditional Lagrangian ray tracing approach needs to solve a system consisting of two ordinary differential equations together with a line integral along the particular particle trajectory. Furthermore, if the velocity data is only available at mesh points, the Lagrangian approach needs to implement interpolation to obtain the velocity and also the velocity gradient at non-mesh points along the particle trajectory taking off from each mesh point, which could be quite time-consuming. Based on the doubling technique, we also propose an efficient iterative Eulerian-type algorithm to identify the longtime LCS for 2D periodic flows. Numerical examples are provided to confirm the accuracy, efficiency and effectiveness of the proposed Eulerian algorithms. </abstract>