Artificial viscosity proper orthogonal decomposition

We introduce improved reduced-order models for turbulent flows. These models are inspired from successful methodologies used in large eddy simulation, such as artificial viscosity, applied to standard models created by proper orthogonal decomposition of flows coupled with Galerkin projection. As a f...

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Bibliographic Details
Published in:Mathematical and computer modelling Vol. 53; no. 1; pp. 269 - 279
Main Authors: Borggaard, Jeff, Iliescu, Traian, Wang, Zhu
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 2011
Elsevier
Subjects:
Artificial viscosity
equations
Exact sciences and technology
Large eddy simulation
Mathematical analysis
Mathematics
methodology
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Partial differential equations
Proper orthogonal decomposition
Sciences and techniques of general use
turbulent flow
viscosity
Proper orthogonal decomposition
Artificial viscosity
Large eddy simulation
Viscosity
Turbulence
Turbulent flow
Decomposition method
Burgers equation
Discretization method
Numerical analysis
Applied mathematics
Diffusion equation
Galerkin method
Abstract space
Mathematical model
Computer aided analysis
ISSN:0895-7177, 1872-9479
Online Access:Get full text
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Summary:We introduce improved reduced-order models for turbulent flows. These models are inspired from successful methodologies used in large eddy simulation, such as artificial viscosity, applied to standard models created by proper orthogonal decomposition of flows coupled with Galerkin projection. As a first step in the analysis and testing of our new methodology, we use the Burgers equation with a small diffusion parameter. We present a thorough numerical analysis for the time discretization of the new models. We then test these models in two problems displaying shock-like phenomena. Of course, since the Burgers equation does not model turbulence, we next need to test our new models in realistic turbulent flow settings. This is the subject of a forthcoming report.
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ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2010.08.015