Lyapunov spectrum of separated flows and its dependence on numerical discretization

TL;DR

This study examines how numerical discretization affects the Lyapunov spectrum of separated flows around an airfoil, revealing that spatial discretization significantly influences chaos levels while time discretization has minimal impact.

Contribution

It provides a detailed analysis of the dependence of Lyapunov spectra on spatial and temporal discretization in separated flow simulations.

Findings

Spatial discretization dramatically affects the Lyapunov spectrum.

Time discretization has a small impact on system dynamics.

Finer meshes do not necessarily lead to more accurate chaos characterization.

Abstract

We investigate the Lyapunov spectrum of separated flows and their dependence on the numerical discretization. The chaotic flow around the NACA 0012 airfoil at low Reynolds number and large angle of attack is considered to that end, and t-, h- and p-refinement studies are performed to examine each effect separately. Numerical results show that the time discretization has a small impact on the dynamics of the system, whereas the spatial discretization can dramatically change them. In particular, the asymptotic Lyapunov spectrum for time refinement is achieved for CFL numbers as large as $\mathcal{O}(10^1-10^2)$, whereas the system continues to become more and more chaotic even for meshes that are much finer than the best practice for this type of flows.