THEORETICAL AND COMPUTATIONAL ANALYSIS OF SPECTRALLY HYPERVISCOUS MODELS OF TURBULENT FLOW

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Xiao, C. (2010). THEORETICAL AND COMPUTATIONAL ANALYSIS OF SPECTRALLY HYPERVISCOUS MODELS OF TURBULENT FLOW. Unc Charlotte Electronic Theses And Dissertations.
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Abstract

Computing turbulent flow is very difficult but forms the basis for computational experiments in Meteorology and Oceanography. To overcome the difficulty and complexity in turbulence computation, a spectrally hyperviscous version of Navier-Stokes equations(SHNSE) has been suggested.The theoretical results that we obtained are the convergence of Galerkin solutions and the continuous dependence on data for the SHNSE, the estimates for the number of determining nodes and determining modes, and the inviscid limit in the case of unforced turbulence. In the computational analysis, Numerical experiments are conducted to validate some of the theoretical properties of the SHNSE and to investigate optimal parameter choices. Numerical results indicate that the SHNSE model has strong potential to be a highly robust platform for studying turbulence which can retain spectral accuracy while significantly reducing the number of degrees of freedom needed for accurate simulation.

Details
Author

Xiao, Chang

Title

THEORETICAL AND COMPUTATIONAL ANALYSIS OF SPECTRALLY HYPERVISCOUS MODELS OF TURBULENT FLOW

Physical Description

1 online resource (104 pages) : PDF

Date

2010

Degree Granting Institution

University of North Carolina at Charlotte

Abstract

Computing turbulent flow is very difficult but forms the basis for computational experiments in Meteorology and Oceanography. To overcome the difficulty and complexity in turbulence computation, a spectrally hyperviscous version of Navier-Stokes equations(SHNSE) has been suggested.The theoretical results that we obtained are the convergence of Galerkin solutions and the continuous dependence on data for the SHNSE, the estimates for the number of determining nodes and determining modes, and the inviscid limit in the case of unforced turbulence. In the computational analysis, Numerical experiments are conducted to validate some of the theoretical properties of the SHNSE and to investigate optimal parameter choices. Numerical results indicate that the SHNSE model has strong potential to be a highly robust platform for studying turbulence which can retain spectral accuracy while significantly reducing the number of degrees of freedom needed for accurate simulation.

Genre

doctoral dissertations

Subjects--Topics

Mathematics

Degree

Ph.D.

Keywords

Determining Modes and Determining Nodes
Galerkin Approximation
Inviscid Limit
Large Eddy Simulation
Spectrally-Hyperviscous Navier-Stokes Equations
Turbulence

Subject Area

Applied Mathematics

Advisor(s)

Avrin, Joel
Deng, Shaozhong

Committee Members

Avrin, Joel
Deng, Shaozhong
Ogunro, Vincent(Tobi)
Zhu, You-Lan

Degree Note

Thesis (Ph.D.)--University of North Carolina at Charlotte, 2010.

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Rights Holder Information

Copyright is held by the author unless otherwise indicated.

Identifier

Xiao_uncc_0694D_10112

Permalink

http://hdl.handle.net/20.500.13093/etd:304