The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows

By G. Berkooz, Philip J. Holmes, John L. Lumley. 1993

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems (2018, methodology): “We then reduce the dimension of the system by proper orthogonal decomposition (POD) [27, 16].”
Discovering governing equations from data by sparse identification of nonlinear dynamical systems (2015, methodology): “The ﬁrst two most energetic POD modes capture a signiﬁcant portion of the energy; the steady-state vortex shedding is a limit cycle in these coordinates.”
Adversarial Uncertainty Quantification in Physics-Informed Neural Networks (2018, background): “However, despite the fact that much progress has been made over the last two decades, the most popular methods for scientific computing under uncertainty, such as polynomial chaos expansions [17, 18, 19], sparse grid quadratures [20, 21], multi-level/multi-fidelity Monte Carlo sampling [22, 23], pro”
A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality (2017, methodology): “Successful applications of the NTFA [58–60], POD [54,55,61,62] and PGD [63] demonstrate the usefulness of these approaches.”
Nonmodal Stability Theory (2007, methodology): “The eigenvalue decomposition of the matrix CG∞CH is known as the Karhunen-Loève (KL), or proper orthogonal decomposition (POD), which has been applied to various turbulent flow fields (Aubry 1991, Berkooz et al. 1993, Sirovich 1987).”
A New Selection Operator for the Discrete Empirical Interpolation Method - Improved A Priori Error Bound and Extensions (2015, methodology): “POD [35, 9] obtains the model reduction basis V from a truncated SVD approximation to a matrix of “snapshots,” a numerically computed trajectory of the full model.”
Reduced order modelling method via proper orthogonal decomposition (POD) for flow around an oscillating cylinder (2010, methodology): “A detailed methodology has already been proposed in the literature (Lumley, 1967; Holmes et al., 1998; Allery, 2002; Berkooz et al., 1993).”
A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations (2010, methodology): “…is classically used as an a posteriori model reduction technique for long-time simulations or parametric analyses of evolution problems [5] [4] [19] [20] [16] [36] [24] [10] [15] [3] In this paper, we focus on the more challenging problem of the a priori construction of such separated…”
Constrained sparse Galerkin regression (2016, background): “These modes may come from a classical expansion, such as Fourier modes, or they may be datadriven, as in the proper orthogonal decomposition (POD) (Berkooz et al., 1993; Sirovich, 1987).”
Generalized spectral decomposition method for solving stochastic finite element equations : Invariant subspace problem and dedicated algorithms (2008, background): “Let us here mention that this kind of decomposition has already been introduced in various domains of application such as functional data analysis [12], image analysis [13], dynamical model reduction [14,15], etc.”