A sensitivity study of the Navier–Stokes-α model

We present a sensitivity study of the Navier Stokes-α model with respect to perturbations of the differential filter length α. The parameter-sensitivity is evaluated using the sensitivity equations method. Once formulated, the sensitivity equations are discretized and computed alongside the NSα model using the same finite elements in space, and Crank–Nicolson in time. We provide a complete stability analysis of the scheme, along with the results of several benchmark problems in both 2D and 3D. We further demonstrate a practical technique to utilize sensitivity calculations to determine the reliability of the NSα model in problem-specific settings. Lastly, we investigate the sensitivity and reliability of important functionals of the velocity and pressure solutions.