Scott-Pomerantz, Colleen Dawn
(2005)
The k-epsilon model in the theory of turbulence.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
We consider the $k-varepsilon$ model in the theory of turbulence, where $k$ is the turbulent kinetic energy, $varepsilon$ is thedissipation rate of the turbulent energy, and $alpha,$ $eta,$ and $gamma$ are positive constants. In particular we examine the Barenblatt self-similar $k-varepsilon$ model, along with boundary conditions taken to ensure the symmetry and compactness of the support of solutions.Under the assumptions:$eta>alpha,$ $3alpha>2eta,$ and $gamma$>3/2,we show the existence of $mu$ for which there is a positive solutionto the system and corresponding boundary conditions by proving a seriesof lemmas. We also include graphs of solutions obtained by using XPPAUT 5.85.
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Details
| Item Type: |
University of Pittsburgh ETD
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| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
31 January 2005 |
| Date Type: |
Completion |
| Defense Date: |
4 December 2004 |
| Approval Date: |
31 January 2005 |
| Submission Date: |
9 December 2004 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
k-epsilon model; existence of solutions; turbulence; shooting methods |
| Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-12092004-201633/, etd-12092004-201633 |
| Date Deposited: |
10 Nov 2011 20:09 |
| Last Modified: |
15 Nov 2016 13:54 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/10241 |
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