Lyapunov spectrum of the separated flow around the NACA 0012 airfoil and its dependence on numerical discretization

Abstract

We investigate the impact of numerical discretization on the Lyapunov spectrum of separated flow simulations. The two-dimensional chaotic flow around the NACA 0012 airfoil at a low Reynolds number and large angle of attack is considered to that end. Time, space and accuracy-order refinement studies are performed to examine each of these effects 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. Also, the finite-time Lyapunov exponents associated to unstable modes are shown to be positively skewed, and quasi-homoclinic tangencies are observed in the attractor of the system. The implications of these results on flow physics and sensitivity analysis of chaotic flows are discussed. Keyword: Computational fluid dynamics; Flow instability; Lyapunov stability analysis; Nonlinear dynamics and chaos; Sensitivity analysis; Separated flows; Turbulence