Uncertainty propagation in CFD using polynomial chaos decomposition

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Dynamically orthogonal field equations for continuous stochastic dynamical systems (2009, background): “[46,47,63,48,64]) are usually derived by substituting a representation as (7) but with the stochastic coefficients given by (23) to the SPDE (8) and then projecting it to the stochastic orthogonal basis functionsΦj(ζ(ω)) using the inner product.”
Fast Numerical Methods for Stochastic Computations: A Review (2009, background): “1), and the examples are for linear problems, the gPC framework can be readily applied to complex problems including the time-dependent and nonlinear ones, for example, Burgers’ equation [34, 94], fluid dynamics [40, 41, 44, 46, 92], flow-structure interactions [96], hyperbolic problems [11,31], mat”
Nonlinear Propagation of Orbit Uncertainty Using Non-Intrusive Polynomial Chaos (2013, methodology): “Although not yet applied in astrodynamics, previous research using PC includes uncertainty quantification in engineering fields such as: fluid dynamics [11–18], solid mechanics [19–22], multibody dynamics [23,24], high-order state estimation [25,26], and many other applications.”