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Numerical Analysis of a Variational Multiscale Method for Turbulence

Kaya, Songul (2005) Numerical Analysis of a Variational Multiscale Method for Turbulence. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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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 [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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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Kaya, Songulsokst20@pitt.eduSOKST20
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairLayton, William Jwjl@pitt.eduWJL
Committee CoChairRiviere,
Committee MemberYotov, Ivanyotov@math.pitt.eduYOTOV
Committee MemberGirault,
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:, etd-12072004-184313
Date Deposited: 10 Nov 2011 20:08
Last Modified: 15 Nov 2016 13:53


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