Uncertainty propagation in CFD using polynomial chaos decomposition

Uncertainty quantification in CFD computations is receiving increased interest, due in large part to the increasing complexity of physical models, and the inherent introduction of random model data. This paper focuses on recent application of PC methods for uncertainty representation and propagation 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 coefficients providing quantitative estimates of the effect of random model data. A general overview of PC applications in CFD is provided, focusing exclusively 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 representations, and a perspective on the applicability of the corresponding techniques to propagate and quantify uncertainty in Navier–Stokes computations.