Stochastic approaches to uncertainty quantification in CFD simulations

By Lionel Mathelin, Y. Hussaini, Thomas A. Zang. Numerical Algorithms, 2005

303 citations recorded by the source corpus.

Subfields: Computational Mechanics, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4b23e3a97f689f0ec24764269b483f17feec48eb

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In Computational Mechanics

In Environmental Engineering

In Statistics and Probability

Citations in the corpus

Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients (2009, background): “Stochastic Collocation has gained much attention recently from the computational community, see for instance the works [3, 10, 23, 20, 32].”
An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008, unknown): “A new numerical technique, which has gained much attention recently by the computational community, is stochastic collocation (see [1, 13, 24, 20, 29]), which can be based on either full or sparse tensor product approximation spaces.”
A compressed sensing approach for partial differential equations with random input data (2012, methodology): “To complete the picture, an alternative trial basis is also considered here: the so-called Stochastic Collocation (SC) approach [2, 31, 49], essentially consists of approximating the”
Probabilistic collocation method for flow in porous media: Comparisons with other stochastic methods (2007, methodology): “A new approach is the stochastic collocation method (SCM) developed by Mathelin et al. [2005] , which has been applied to problems with small number of random variables.”
Digital Twin: Values, Challenges and Enablers From a Modeling Perspective (2019, background): “…ROMs (i.e., emulators) have great promise for applications especially when multiple forward full-order numerical simulations are required (e.g., data assimilation [254]–[259], parameter identiﬁcation [260]– [263], uncertainty quantiﬁcation [264]–[270], optimization and control [271]–[278]).”
Efficient and Accurate Quantification of Uncertainty for Multiphase Flow With the Probabilistic Collocation Method (2009, methodology): “The Galerkin method is used usually to solve for the coefficients in polynomial chaos expansions (Ghanem 1998; Xiu and Karniadakis 2002; Mathelin et al. 2005) and leads to a set of coupled equations governing those coefficients.”
Design of Composite Wings Including Uncertainties : A Probabilistic Approach (2009, methodology): “PCE is a method that has been used to explore the variability of response in control [23,24], computational fluid dynamics [25,26], and buckling problems [27].”
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007, background): “Stochastic collocation has already been applied in a variety of problems and is the subject of ongoing research; see, among others, [54, 42] and the recent work [61], which the authors became aware of upon completion of this work.”
A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008, unknown): “We mention, among others, the Spectral Galerkin method [3, 4, 16, 20, 22, 25, 27, 36], Stochastic Collocation [5, 24, 29, 35], perturbation methods or Neumann expansions [1, 17,30,34].”