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.