Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics. (English) Zbl 1168.76041

Najm, Habib N.

Davis, Stephen H. (ed.) et al., Annual review of fluid mechanics. Vol. 41. Palo Alto, CA: Annual Reviews (ISBN 978-0-8243-0741-7/hbk). Annual Review of Fluid Mechanics 41, 35-52 (2009).

Summary: The quantification of uncertainty in computational fluid dynamics (CFD) predictions is both a significant challenge and an important goal. Probabilistic uncertainty quantification (UQ) methods have been used to propagate uncertainty from model inputs to outputs when input uncertainties are large and have been characterized probabilistically. Polynomial chaos (PC) methods have found increased use in probabilistic UQ over the past decade. This review describes the use of PC expansions for the representation of random variables/fields and discusses their utility for the propagation of uncertainty in computational models, focusing on CFD models. Many CFD applications are considered, including flows in porous media, incompressible and compressible flows, and thermofluid and reacting flows. The review examines each application area, focusing on the demonstrated use of PC, UQ and the associated challenges. Cross-cutting challenges with time unsteadiness and long-time horizons are also discussed.
For the entire collection see [Zbl 1155.76006].

MSC:

76M99	Basic methods in fluid mechanics
76M35	Stochastic analysis applied to problems in fluid mechanics
76-02	Research exposition (monographs, survey articles) pertaining to fluid mechanics

Keywords:

random variables; time unsteadiness; long-time horizons