Stability Properties of POD–Galerkin Approximations for the Compressible Navier–Stokes Equations

By Angelo Iollo, Stéphane Lanteri, Jean-Antoine Desideri. 2000

244 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/30fef2024bbf7b69b5d2177476823cfa33bef608

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In Computational Mechanics

In Statistical and Nonlinear Physics

Citations in the corpus

Non-linear Petrov-Galerkin methods for reduced order modelling of the Navier-Stokes equations using a mixed finite element pair (2013, methodology): “Angelo et al. [20] [21] proposed two stabilization methods for POD/ROM: one that relies on the explicit addition of an artificial dissipation term whose construction is similar to that of the Lax–Wendroff scheme; another one that consists in constructing the POD for both function and gradient values”
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives (2014, unknown): “Similarly, the H1 inner product was recommended for the computation of POD modes for compressible Navier-Stokes equations in [66] for the purpose of enhancing stability.”
A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations (2010, unknown): “L 2 (Ω) or H 1 (Ω) [17].”
Free-form-deformation parameterization for multilevel 3D shape optimization in aerodynamics (2003, methodology): “With this respect, we propose as a necessary step, to either hybridize genetic algorithm [36] to speed up its convergence, or to use interpolation techniques [2], reduced model for flow problem [15] or neural networks [18].”
Calibration of POD reduced‐order models using Tikhonov regularization (2009, background): “i) the structural instability of the Galerkin projection [20, 21, 14], ii) the truncation of the POD basis (dissipative scales associated to higher POD modes are not sufficiently present in the model), iii) the fact that the set of data does not perfectly respect the weak formulation (5): inaccurate”
On closures for reduced order models—A spectrum of first-principle to machine-learned avenues (2021, unknown): “(53) for the components of ~ B and ~ L .”