On the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics

In this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams. The method is quite...

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Bibliographic Details
Published in:Journal of scientific computing Vol. 73; no. 1; pp. 157 - 177
Main Authors: Pitton, Giuseppe, Rozza, Gianluigi
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2017
Springer Nature B.V
Subjects:
Algorithms
Approximation
Bifurcations
Boundary conditions
Cavity flow
Computational Mathematics and Numerical Analysis
Computing time
Dynamic stability
Flow stability
Fluid dynamics
Fluid flow
Fluid mechanics
Incompressible flow
Incompressible fluids
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Reduced order models
Reynolds number
Theoretical
Velocity
Vortices
Flow stability
Proper orthogonal decomposition
Steady bifurcation
Navier–Stokes
Spectral element method
Hopf bifurcation
Reduced basis method
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary:In this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams. The method is quite general since it can in principle be specialized to a wide class of nonlinear problems, but in this work we focus on an application in incompressible fluid dynamics at low Reynolds numbers. The validation of the reduced order model with the full order computation for a benchmark cavity flow problem is promising.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-017-0419-6