Spectral Methods for Uncertainty Quantification : With Applications to Computational Fluid Dynamics This book presents applications of spectral methods to problems of uncertainty propagation and quantification in model based computations focusing on the computational and algorithmic features of these methods most useful in dealing with models based on partial differential equations in particular models arising in simulations of fluid flows. Spectral stochastic methods are probabilistic in nature and are consequently rooted in the rich mathematical foundations associated with probability and measure spaces. A brief discussion is provided of only those theoretical aspects needed to set the