POD and CVT-based reduced-order modeling of Navier-Stokes flows

By J. Burkardt, Max D. Gunzburger, Hyung-C. Lee. 2006

286 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/10facac9978dba39656cb6f8ab32e52302f2c487

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In Computational Mechanics

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Citations in the corpus

Supremizer stabilization of POD–Galerkin approximation of parametrized steady incompressible Navier–Stokes equations (2015, background): “In this paper, we consider the latter [11, 26, 35, 36].”
Computational Reduction for Parametrized PDEs: Strategies and Applications (2012, background): “Clearly, during the Online stage, the reduced problem can be solved for parameter instances μ ∈ D not selected during the Offline stage, and even extrapolating the solution for values μ ∈ Dext belonging to a parameter superset Dext ⊇ D [9].”
Cluster-based reduced-order modelling of a mixing layer (2013, methodology): “The close relation between CVTs and k-means algorithm was already mentioned in Burkardt et al. (2006a).”
PGD-Based Computational Vademecum for Efficient Design, Optimization and Control (2013, background): “5], E ∈ [5,500] (GPa) and e ∈ [5,20] (mm) that allow to describe a large variety of isotropic material: plastics, metals, alloys, .”
Non-intrusive reduced order modeling of nonlinear problems using neural networks (2018, background): “As a result, it may show severe instabilities [8].”
Advances in Studies and Applications of Centroidal Voronoi Tessellations (2010, methodology): “The CVOD concept has been further studied in [11, 12, 78, 104] for a variety of physical models including the nonlinear Burger’s equation and the Navier-Stokes equations.”
REDUCED BASIS APPROXIMATION AND A POSTERIORI ERROR ESTIMATION FOR THE PARAMETRIZED UNSTEADY BOUSSINESQ EQUATIONS (2011, background): “However, none of the earlier examples of reduced order models for the unsteady incompressible NavierStokes and Boussinesq equations [7,9,12,22,23,30–33] is endowed with practicable and rigorous error bounds.”
Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation (2009, background): “Although there are many examples of reduced order models for the unsteady incompressible Navier–Stokes equations [5,7,9,13,14,17–21], none is endowed with rigorous a posteriori error bounds.”
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives (2014, methodology): “We conclude this section by mentioning also some additional techniques quite close to POD for generating efficiently reduced spaces, the Centroidal Voronoi Tessellation (CVT) [25, 26, 46] and the Proper Generalized Decomposition (PGD) method [92], which has been recently applied to the solution of N”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, background): “The work [33] discusses details of CVT-based basis construction.”