Model reduction for compressible flows using POD and Galerkin projection

By Clarence W. Rowley, Tim Colonius, Richard M. Murray. 2004

913 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/110e14bb261dff117eb51aebc70683ab79578be7

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In Computational Mechanics

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

Active control of flow-induced cavity oscillations (2008, methodology): “[116] for a thorough description of the method for compressible flows.”
On closures for reduced order models—A spectrum of first-principle to machine-learned avenues (2021, neutral): “(54) with physical constraints to enforce the regressed matrix and tensor to have similar characteristics as the GROM operators (e.g., ~ L being negative semi-deﬁnite and ~ N being energy conserving).”
Efficient non‐linear model reduction via a least‐squares Petrov–Galerkin projection and compressive tensor approximations (2011, background): “Lack of optimality can lead to the undesirable property of deterioration in solution quality as the approximation spaces expand, as has been observed in [32], for example.”
Nonlinear Model Reduction via Discrete Empirical Interpolation (2010, methodology): “The POD-Galerkin approach has provided reduced-order models of systems in numerous applications such as compressible flow [38], fluid dynamics [23], aerodynamics [9], and optimal control [22].”
Generalizing Koopman Theory to Allow for Inputs and Control (2016, neutral): “On these lowdimensional subspaces, controllers can be described, constructed, and implemented [35, 23, 19, 41, 40, 39, 53, 17].”
Modal Analysis of Fluid Flows: An Overview (2017, methodology): “POD modes have been used to construct Galerkin projection-based reducedorder models for incompressible [48,55–57] and compressible [58] flows.”
Proportional Closed-Loop Feedback Control of Flow Separation (2007, background): “[15] to include the dynamically important information contained in a compressible flow.”
Stabilization of projection-based reduced order models for linear time-invariant systems via optimization-based eigenvalue reassignment (2014, background): “, systems with more than 10,000 degrees of freedom (dofs) [12]).”
Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis (2017, background): “Many papers exclusively present space-only POD (Sirovich, 1989; Moin & Moser, 1989; Holmes et al., 1997; Chatterjee, 2000; Rowley et al., 2004; Cordier & Bergmann, 2008; Rowley & Dawson, 2017), while one early review (George, 1988) considers only spectral POD.”
Model Reduction for fluids, Using Balanced Proper Orthogonal Decomposition (2005, background): “The POD modes of the dataset X with respect to this inner product are eigenvectors of R = XX * W o (see [Rowley et al., 2004] for an explanation of POD with respect to an arbitrary inner product).”
Modeling of transitional channel flow using balanced proper orthogonal decomposition (2007, methodology): “The POD/Galerkin method has been used extensively for reduced-order modeling of fluid problems [13, 23, 31, 34, 35].”
Model Reduction via Proper Orthogonal Decomposition (2008, background): “in fluid dynamics [4, 14, 32, 35, 36] as well as in signal analysis and pattern recognition [9, 33].”