Reduced-basis modeling of turbulent plane channel flow

Johansson, Peter S.; Andersson, Helge I.; Rønquist, Einar M.

doi:10.1016/j.compfluid.2004.11.005

Cited by 12 publications

(10 citation statements)

References 23 publications

(30 reference statements)

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“…This feature can be exploited in a reduced order model. The reduced order model can often capture the system behavior accurately; examples from fluid dynamics include [10,12,13,24,27,[31][32][33]35]. Furthermore, at least for systems with only quadratic nonlinearities -such as the Boussinesq equations -the reduced order model can be significantly less costly than classical discretization techniques such as the finite element method.…”

Section: Introductionmentioning

confidence: 99%

REDUCED BASIS APPROXIMATION AND A POSTERIORI ERROR ESTIMATION FOR THE PARAMETRIZED UNSTEADY BOUSSINESQ EQUATIONS

Knezevic

Nguyen

Patera

2011

Math. Models Methods Appl. Sci.

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In this paper we present reduced basis approximations and associated rigorous a posteriori error bounds for the parametrized unsteady Boussinesq equations. The essential ingredients are Galerkin projection onto a low-dimensional space associated with a smooth parametric manifold -to provide dimension reduction; an efficient POD-Greedy sampling method for identification of optimal and numerically stable approximationsto yield rapid convergence; accurate (Online) calculation of the solution-dependent stability factor by the Successive Constraint Method -to quantify the growth of perturbations/residuals in time; rigorous a posteriori bounds for the errors in the reduced basis approximation and associated outputs -to provide certainty in our predictions; and an Offline-Online computational decomposition strategy for our reduced basis approximation and associated error bound -to minimize marginal cost and hence achieve high performance in the real-time and many-query contexts. The method is applied to a transient natural convection problem in a two-dimensional "complex" enclosure -a square with a small rectangle cut-out -parametrized by Grashof number and orientation with respect to gravity. Numerical results indicate that the reduced basis approximation converges rapidly and that furthermore the (inexpensive) rigorous a posteriori error bounds remain practicable for parameter domains and final times of physical interest.

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Section: Introductionmentioning

confidence: 99%

REDUCED BASIS APPROXIMATION AND A POSTERIORI ERROR ESTIMATION FOR THE PARAMETRIZED UNSTEADY BOUSSINESQ EQUATIONS

Knezevic

Nguyen

Patera

2011

Math. Models Methods Appl. Sci.

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“…There are examples of rigorous reduced basis a posteriori error bounds for the steady Burgers' [37] and incompressible Navier-Stokes [28,36] equations; the new contribution of the current paper is treatment of the unsteady -paraboliccase. Although there are many examples of reduced order models for the unsteady incompressible Navier-Stokes equations [5,7,9,13,14,[17][18][19][20][21], none is endowed with rigorous a posteriori error bounds.…”

Section: Introductionmentioning

confidence: 99%

Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation

Nguyen

Rozza

Patera

2009

Calcolo

113

130

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“…The first applications of POD were concerned with the analysis of turbulent flows and date back to the early '90s [1,2]; more recent applications can be found, for instance, in [22,25,27,30], as well as in [9,12,20] for parametrized flows.…”

Section: Alternative Approachesmentioning

confidence: 99%

Computational Reduction for Parametrized PDEs: Strategies and Applications

2012

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Abstract. In this paper we present a compact review on the mostly used techniques for computational reduction in numerical approximation of partial differential equations. We highlight the common features of these techniques and provide a detailed presentation of the reduced basis method, focusing on greedy algorithms for the construction of the reduced spaces. An alternative family of reduction techniques based on surrogate response surface models is briefly recalled too. Then, a simple example dealing with inviscid flows is presented, showing the reliability of the reduced basis method and a comparison between this technique and some surrogate models.Mathematics Subject Classification (2010). Primary 78M34; Secondary 49J20, 65N30, 76D55.

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Reduced-basis modeling of turbulent plane channel flow

Cited by 12 publications

References 23 publications

REDUCED BASIS APPROXIMATION AND A POSTERIORI ERROR ESTIMATION FOR THE PARAMETRIZED UNSTEADY BOUSSINESQ EQUATIONS

REDUCED BASIS APPROXIMATION AND A POSTERIORI ERROR ESTIMATION FOR THE PARAMETRIZED UNSTEADY BOUSSINESQ EQUATIONS

Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation

Computational Reduction for Parametrized PDEs: Strategies and Applications

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