Analysis of nonlinear spectral eddy-viscosity models of turbulence

Max Gunzburger; Eunjung Lee; Yuki Saka; Catalin Trenchea; Xiaoming Wang

doi:10.1007/s10915-009-9335-8

Analysis of nonlinear spectral eddy-viscosity models of turbulence

Max Gunzburger, Eunjung Lee, Yuki Saka, Catalin Trenchea, Xiaoming Wang

Department of Computational Science and Engineering

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

Fluid turbulence is commonly modeled by the Navier-Stokes equations with a large Reynolds number. However, direct numerical simulations are not possible in practice, so that turbulence modeling is introduced. We study artificial spectral viscosity models that render the simulation of turbulence tractable. We show that the models are well posed and have solutions that converge, in certain parameter limits, to solutions of the Navier-Stokes equations. We also show, using the mathematical analyses, how effective choices for the parameters appearing in the models can be made. Finally, we consider temporal discretizations of the models and investigate their stability.

Original language	English
Pages (from-to)	294-332
Number of pages	39
Journal	Journal of Scientific Computing
Volume	45
Issue number	1-3
DOIs	https://doi.org/10.1007/s10915-009-9335-8
Publication status	Published - 2010 Oct

Bibliographical note

Funding Information:
Acknowledgements This paper is based on part of Yuki Saka’s Ph.D. dissertation written under the direction of MDG and XW. This work is supported in part by the grants from the Air Force Office of Scientific Research FA9550-08-1-0415 (MG and EL) and FA9550-09-1-0058 (CT) and the National Science Foundation DMS-0606671 (XW).

All Science Journal Classification (ASJC) codes

Software
Theoretical Computer Science
Numerical Analysis
General Engineering
Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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10.1007/s10915-009-9335-8

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title = "Analysis of nonlinear spectral eddy-viscosity models of turbulence",

abstract = "Fluid turbulence is commonly modeled by the Navier-Stokes equations with a large Reynolds number. However, direct numerical simulations are not possible in practice, so that turbulence modeling is introduced. We study artificial spectral viscosity models that render the simulation of turbulence tractable. We show that the models are well posed and have solutions that converge, in certain parameter limits, to solutions of the Navier-Stokes equations. We also show, using the mathematical analyses, how effective choices for the parameters appearing in the models can be made. Finally, we consider temporal discretizations of the models and investigate their stability.",

keywords = "Eddy-viscosity models, Navier-Stokes equations, Spectral methods, Turbulence",

author = "Max Gunzburger and Eunjung Lee and Yuki Saka and Catalin Trenchea and Xiaoming Wang",

note = "Funding Information: Acknowledgements This paper is based on part of Yuki Saka{\textquoteright}s Ph.D. dissertation written under the direction of MDG and XW. This work is supported in part by the grants from the Air Force Office of Scientific Research FA9550-08-1-0415 (MG and EL) and FA9550-09-1-0058 (CT) and the National Science Foundation DMS-0606671 (XW).",

year = "2010",

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AU - Gunzburger, Max

AU - Lee, Eunjung

AU - Saka, Yuki

AU - Trenchea, Catalin

AU - Wang, Xiaoming

N1 - Funding Information: Acknowledgements This paper is based on part of Yuki Saka’s Ph.D. dissertation written under the direction of MDG and XW. This work is supported in part by the grants from the Air Force Office of Scientific Research FA9550-08-1-0415 (MG and EL) and FA9550-09-1-0058 (CT) and the National Science Foundation DMS-0606671 (XW).

PY - 2010/10

Y1 - 2010/10

N2 - Fluid turbulence is commonly modeled by the Navier-Stokes equations with a large Reynolds number. However, direct numerical simulations are not possible in practice, so that turbulence modeling is introduced. We study artificial spectral viscosity models that render the simulation of turbulence tractable. We show that the models are well posed and have solutions that converge, in certain parameter limits, to solutions of the Navier-Stokes equations. We also show, using the mathematical analyses, how effective choices for the parameters appearing in the models can be made. Finally, we consider temporal discretizations of the models and investigate their stability.

AB - Fluid turbulence is commonly modeled by the Navier-Stokes equations with a large Reynolds number. However, direct numerical simulations are not possible in practice, so that turbulence modeling is introduced. We study artificial spectral viscosity models that render the simulation of turbulence tractable. We show that the models are well posed and have solutions that converge, in certain parameter limits, to solutions of the Navier-Stokes equations. We also show, using the mathematical analyses, how effective choices for the parameters appearing in the models can be made. Finally, we consider temporal discretizations of the models and investigate their stability.

KW - Eddy-viscosity models

KW - Navier-Stokes equations

KW - Spectral methods

KW - Turbulence

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JO - Journal of Scientific Computing

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Analysis of nonlinear spectral eddy-viscosity models of turbulence

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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