Turbulence model uncertainty estimation via Monte Carlo perturbation of the Reynolds Stress Tensor

We propose to rely on a flat Dirichlet distribution to sample the eigenvalues of the Reynolds Stress Tensor in RANS simulations. The goal is to forward propagate the uncertainty inherent the structure of the turbulence closure to targeted QoIs. The flat Dirichlet distribution is defined over the 2-dimensional simplex delimiting the Reynolds Stress Tensor realizability conditions. This ensures the tensor positive-definiteness and serves the uncertainty forward propagation by means of diverse techniques e.g., Monte Carlo or Polynomial Chaos Expansions. Simulations are performed using a modified version of the open-source SU2 suite. Results are obtained for two reference test cases. Namely, the subsonic air flow over a backward facing step and the NACA0012 airfoil operating in subsonic conditions and with a variable angle of attack.