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This work describes a new method for building a statistical model for the structural uncertainties in the k ! turbulence model. An inverse RANS problem is solved using the adjoint method to determine the turbulent viscosity that produces the ow eld closest to that predicted by direct numerical simulation. We describe the dierence in the turbulent viscosity eld inferred by the inverse RANS problem and turbulent viscosity eld predicted by RANS as a Gaussian random eld, and develop a statistical model of this random eld using maximum likelihood estimation. The resulting statistical model is used to propagate uncertainty to engineering quantities of interest using non-intrusive techniques. Results for turbulent ow in a periodic straight walled channel are presented and analyzed.
Dow et al. (Mon,) studied this question.