Numerical solution of parametrized Navier–Stokes equations by reduced basis methods

By Alfio Maria Quarteroni, Gianluigi Rozza. 2007

169 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2f8fab9e22ff1a7f8923d28933f8df295350014f

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In Computational Mechanics

In Mechanics of Materials

In Statistical and Nonlinear Physics

Citations in the corpus

Supremizer stabilization of POD–Galerkin approximation of parametrized steady incompressible Navier–Stokes equations (2015, unknown): “See, for example, [16] for further details.”
An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier–Stokes flows (2014, background): “This has been further developed in more recent years [7, 8] by considering a complete natural norm framework, whereas a first case of simple nonaffine geometrical parametrizations can be found in [23].”
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives (2014, unknown): “[87, 100, 109] for their complete derivation.”
POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder (2017, unknown): “The third order tensor Cijk is stored [30,31] to deal with the non-linear term in the present work.”
Computational Reduction for Parametrized PDEs: Strategies and Applications (2012, unknown): “in [14,34,44,50,54].”
Certified reduced basis approximation for parametrized partial differential equations and applications (2011, background): “Classical problems arising in applied sciences are, for example, Navier-Stokes/Boussinesq and Burgers’ equations in fluid mechanics [16, 18, 59, 17, 60, 47, 48] and nonlinear elasticity in solid mechanics.”
Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations (2007, background): “(We also address here the constuction of div-stable [26, 27] RB (Navier)-Stokes approximations [122, 136].”