Asymptotic inference for nearly unstable AR(p) processes

In this paper nearly unstable AR( p) processes (in other words, models with characteristic roots near the unit circle) are studied. Our main aim is to describe the asymptotic behavior of the least-squares estimators of the coefficients. A convergence result is presented for the general complex-valued case, The limit distribution is given by the help of some continuous time AR processes. We apply the results for real-valued nearly unstable AR(p) models. In this case the limit distribution can be identified with the maximum likelihood estimator of the coefficients of the corresponding continuous time AR processes

Numerical simulation of transitional flow on a wind turbine airfoil with RANS-based transition model

This paper presents a numerical investigation of transitional flow on the wind turbine airfoil DU91-W2-250 with chord-based Reynolds number Rec = 1.0 × 106. The Reynolds-averaged Navier–Stokes based transition model using laminar kinetic energy concept, namely the k − kL − ω model, is employed to resolve the boundary layer transition. Some ambiguities for this model are discussed and it is further implemented into OpenFOAM-2.1.1. The k − kL − ω model is first validated through the chosen wind turbine airfoil at the angle of attack (AoA) of 6.24° against wind tunnel measurement, where lift and drag coefficients, surface pressure distribution and transition location are compared. In order to reveal the transitional flow on the airfoil, the mean boundary layer profiles in three zones, namely the laminar, transitional and fully turbulent regimes, are investigated. Observation of flow at the transition location identifies the laminar separation bubble. The AoA effect on boundary layer transition over wind turbine airfoil is also studied. Increasing the AoA from −3° to 10°, the laminar separation bubble moves upstream and reduces in size, which is in close agreement with wind tunnel measurement

Rosenbrock time integration for unsteady flow simulations

This contribution compares the efficiency of Rosenbrock time integration schemes with ESDIRK schemes, applicable to unsteady flow and fluid-structure interaction simulations. Compared to non-linear ESDIRK schemes, the linear implicit Rosenbrock- Wanner schemes require subsequent solution of the same linear systems with different right hand sides. By solving the linear systems with the iterative solver GMRES, the preconditioner can be reused for the subsequent stages of the Rosenbrock-Wanner scheme. Unsteady flow simulations show a gain in computational efficiency of approximately factor three to five in comparison with ESDIRK