Uncertainty Propagation in CFD Using Polynomial Chaos Decomposition

Uncertainty quantication (UQ) in CFD computations is receiving increased in-terest, due in large part to the increasing complexity of physical models, and the inherent introduction of random model data. This paper focuses on recent applica-tion of Polynomial Chaos (PC) methods for uncertainty representation and propa-gation in CFD computations. The fundamental concept on which Polynomial Chaos (PC) representations are based is to regard uncertainty as generating a new set of dimensions, and the solution as being dependent on these dimensions. A spectral decomposition in terms of orthogonal basis functions is used, the evolution of the basis coecients providing quantitative estimates of the eect of random model data. A general overview of PC applications in CFD is provided, focusing exclu-sively on applications involving the unreduced Navier-Stokes equations. Included in the present review are an exposition of the mechanics of PC decompositions, an illustration of various means of implementing these representation, a perspec-tive on the applicability of the corresponding techniques to propagate and quantify uncertainty in Navier-Stokes computations