Enablers for robust POD models

By M. Bergmann, Charles-Henri Bruneau, Angelo Iollo. Journal of Computational Physics, 2009

330 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/13ee73dceb5dd30454c03537af8d0cae505e9a04

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Citations in the corpus

Supremizer stabilization of POD–Galerkin approximation of parametrized steady incompressible Navier–Stokes equations (2015, background): “Further details about other possible approaches can be found, for instance, in [7, 8].”
POD-Galerkin method for finite volume approximation of Navier–Stokes and RANS equations (2016, methodology): “On the other hand, in some cases it is not possible to eliminate this term, hence some additional terms [56] or the construction of a basis for the pressure are needed [44].”
POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder (2017, methodology): “• Differently to what proposed in [21, 5], where only the momentum equation is considered and where it is assumed that velocity and pressure share the same temporal coefficients, the Poisson equation for pressure reported in Equation (2.”
Modal Analysis of Fluid Flows: Applications and Outlook (2019, methodology): “the target of subgrid-scale modeling in large eddy simulations. Research has examined the construction of mixing length [54], Smagorinsky-type [251,256{258], and variational multiscale (VMS) closures [251,259,260]. Another approach that displays similarities to the variational multiscale method is t”
Stabilization of projection-based reduced order models for linear time-invariant systems via optimization-based eigenvalue reassignment (2014, methodology): “The stabilization of ROMs using shift modes and residual modes was proposed in [37,38] by Noack et al.”
Proper orthogonal decomposition closure models for turbulent flows: A numerical comparison (2011, methodology): “We note that a fundamentally different VMS LES closure model that utilizes the NSE residual was proposed in Bazilevs et al. (2007); this model was used in a POD setting in Bergmann et al. (2009).”
On closures for reduced order models—A spectrum of first-principle to machine-learned avenues (2021, neutral): “A two-scale decomposition of the ﬂow ﬁeld into resolved and unresolved scales was used by Bergmann et al. 256 to develop a VMS ROM closure model with a residual based eddy viscosity component.”
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives (2014, methodology): “For a review of various stabilization methods for Galerkin ROMS we refer to [16].”