Spectral Methods for Uncertainty Quantification : With Applications to Computational Fluid Dynamics

by Le Maitre, O. P.; Knio, O. M.

• ISBN13: 9789048135196
• ISBN10: 9048135192
• Edition: 1st
• Format: Hardcover
• Copyright: 2010-06-30
• Publisher: Springer Verlag

Summary

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. The practical implementation of these methods is demonstrated in applications to elementary problems, as well as in more elaborate examples selected from the authors' interests in incompressible vortex-dominated flows and compressible flows at low Mach numbers.Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundations associated with probability and measure spaces. Despite the authors' fascination with these foundations, only those theoretical aspects needed to set the stage for subsequent applications are discussed. Readers are assumed to be familiar with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral method is naturally helpful but not essential.