A spectral viscosity method for correcting the long-term behavior of POD models

By Sirod Sirisup, G. Em Karniadakis. 2004

208 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3e5c9292848b861f2759f59e2d515c223702ebb3

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In Computational Mechanics

In Statistical and Nonlinear Physics

Citations in the corpus

Proper orthogonal decomposition closure models for turbulent flows: A numerical comparison (2011, methodology): “For more details, the reader is referred to Sirovich (1987); Holmes et al.”
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives (2014, methodology): “The idea was further developed by extending the spectral vanishing viscosity method of Tadmor [115] to the Navier-Stokes equations in [111].”
To appear in the ACM SIGGRAPH conference proceedings Modular Bases for Fluid Dynamics (unknown): “Model reduction is also a topic of active research in the field of computational fluid dynamics and applied mathematics, where the technique is known as proper orthogonal decomposition (POD), Karhunen-Loéve decomposition, or subspace integration [Holmes et al. 1996; Rowley et al. 2006; Ausseur et al”
On the stability and extension of reduced-order Galerkin models in incompressible flows (2009, methodology): “In the POD model of the flow past a cylinder, Sirisup and Karniadakis [ 36 ] showed that the onset of divergence from the correct limit cycle depends on the number of modes in the Galerkin expansion, the Reynolds number, and the flow geometry.”
Model reduction for real-time fluids (2006, methodology): “After a long-time integration of dissipative flows, POD-based simulation methods exhibit drifting inaccuracies that have been handled with non-linear Galerkin projection [Marion and Temam 1989] and viscosity method correction [Sirisup and Karniadakis 2004].”
Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition (2009, methodology): “Unlike the experiences reported in the literature (see e.g. Noack et al. 2003; Sirisup & Karniadakis 2004; Bergmann et al. 2005), we have not observed any numerical instability after integration over a number of vortex shedding periods.”