A stochastic projection method for fluid flow. I: basic formulation

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Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators (2006, background): “In the last period of fifteen years, a lot of works have been carried out in this area, in particular concerning the stochastic finite element method [14, 19−26, 39, 46, 69, 82, 84, 85, 87, 89] and other numerical methods for solving stochastic boundary value problems [11, 43, 44].”
Coherence motivated sampling and convergence analysis of least squares polynomial Chaos regression (2014, methodology): “Thermally Driven Cavity Flow Following [34, 2, 35, 36], we next consider a 2-D heat driven square cavity flow problem with uncertain wall temperature, as shown in Fig.”
Stochastic spectral methods for efficient Bayesian solution of inverse problems (2005, unknown): “[20,32] extended these techniques to thermo-fluid systems.”
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”
Uncertainty propagation using Wiener-Haar expansions (2004, methodology): “Exploiting the orthogonality of the basis, we obtain the following coupled system [ 12 ,13]:”