Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics

TLDR

Uncertainty quantification in CFD is a major challenge, with probabilistic UQ methods—particularly polynomial chaos—growing in use to propagate input uncertainties to outputs. This review investigates how polynomial‑chaos expansions represent random variables and fields to propagate uncertainty in CFD models. It surveys PC‑UQ applications across porous, incompressible, compressible, thermofluid, and reacting flows, highlighting demonstrated use, challenges, and issues of time‑unsteadiness and long horizons.

Abstract

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 flow 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.