An improved Eulerian approach for the finite time Lyapunov exponent

DOI10.1007/s10915-018-0669-yzbMath1417.65156OpenAlexW2791673777MaRDI QIDQ1785495

Shingyu Leung, Guoqiao You

Publication date: 28 September 2018

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-018-0669-y

zbMATH Keywords

coherent structurespartial differential equationsflow visualizationfinite time Lyapunov exponentflow maps

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Numerical problems in dynamical systems (65P99)

Related Items

Computing the finite time Lyapunov exponent for flows with uncertainties ⋮ Eulerian algorithms for computing some Lagrangian flow network quantities ⋮ Eulerian Algorithms for Computing the Forward Finite Time Lyapunov Exponent Without Finite Difference upon the Flow Map ⋮ Within-Cluster Variability Exponent for Identifying Coherent Structures in Dynamical Systems ⋮ Uncertainty in finite-time Lyapunov exponent computations ⋮ Sparse subsampling of flow measurements for finite-time Lyapunov exponent in domains with obstacles ⋮ Fast construction of forward flow maps using Eulerian based interpolation schemes ⋮ Fast Computations for the Lagrangian-averaged Vorticity Deviation Based on the Eulerian Formulations

Uses Software

• VIALS

Cites Work

• Unnamed Item
• VIALS: an Eulerian tool based on total variation and the level set method for studying dynamical systems
• An Eulerian approach for computing the finite time Lyapunov exponent
• Fast geodesics computation with the phase flow method
• Eulerian Gaussian beams for Schrödinger equations in the semi-classical regime
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Weighted essentially non-oscillatory schemes
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Eulerian based interpolation schemes for flow map construction and line integral computation with applications to Lagrangian coherent structures extraction
• Lagrangian coherent structures and mixing in two-dimensional turbulence
• Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows
• The backward phase flow method for the Eulerian finite time Lyapunov exponent computations
• The local projection $P^0-P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
• Lagrangian coherent structures in n-dimensional systems
• Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence
• Visualization of Coherent Structures in Transient 2D Flows
• Total variation diminishing Runge-Kutta schemes
• Accurate extraction of Lagrangian coherent structures over finite domains with application to flight data analysis over Hong Kong International Airport
• The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds
• Lagrangian coherent structures and internal wave attractors
• A Local Level Set Method for Paraxial Geometrical Optics
• Eulerian Methods for Visualizing Continuous Dynamical Systems using Lyapunov Exponents
• Distinguished material surfaces and coherent structures in three-dimensional fluid flows