Kaya, Songul
(2005)
Numerical Analysis of a Variational Multiscale Method for Turbulence.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
This thesis is concerned with one of the most promising approaches to the numerical simulation of turbulent flows, the subgrid eddy viscosity models. We analyze both continuous and discontinuous finite element approximation of the new subgrid eddy viscosity model introduced in [43], [45], [44].First, we present a new subgrid eddy viscosity model introduced in a variationally consistent manner and acting only on the small scales of the fluid flow. We give complete convergence of themethod. We show convergence of the semi-discrete finite element approximation of the model and give error estimates of the velocity and pressure. In order to establish robustness of themethod with respect to Reynolds number, we consider the Oseen problem. We present the error is uniformly bounded with respect to the Reynolds number.Second, we establish the connection of the new eddy viscosity model with another stabilization technique, called VariationalMultiscale Method (VMM) of Hughes et.al. [35]. We then show the advantages of the method over VMM. The new approach defines mean by elliptic projection and this definition leads to nonzerofluctuations across element interfaces.Third, we provide a careful numerical assessment of a new VMM. We present how this model can be implemented in finite element procedures. We focus on herein error estimates of the model andcomparison to classical approaches. We then establish that the numerical experiments support the theoretical expectations.Finally, we present a discontinuous finite element approximation of subgrid eddy viscosity model. We derive semi-discrete and fullydiscrete error estimations for the velocity.
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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Unpublished |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: |
4 February 2005 |
| Date Type: |
Completion |
| Defense Date: |
21 October 2004 |
| Approval Date: |
4 February 2005 |
| Submission Date: |
7 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: |
Discontinuous Galerkin Method; Finite element method; Subgrid eddy viscosity; Time dependent Navier Stokes; Variational multiscale method; Error analysis |
| Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-12072004-184313/, etd-12072004-184313 |
| Date Deposited: |
10 Nov 2011 20:08 |
| Last Modified: |
15 Nov 2016 13:53 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/10125 |
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