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Iuliana, Stanculescu (2008) TURBULENCE MODELING AS AN ILL-POSEDPROBLEM. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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This thesis is concerned with the derivation and mathematical analysis of new turbulencemodels, based on methods for solving ill-posed problems.Turbulence causes the formation of eddies of many different length scales. Small, unresolved scales have deterministic roles in the statistics of the resolved scales. The main problem of computational turbulence is to accurately represent the effect of the unknownsmall scales upon the observable large scales. This is really just another ill-posed problemand the work in this thesis shows that excellent turbulence models do come from standardmethods for ill-posed problems. Large Eddy Simulation (LES) exploits this decoupling ofscales in a turbulent flow: the larger unsteady turbulent motions are directly represented,while the effects of the smaller scale motions are modeled. This is achieved by introducing afiltering operation, which depends on a chosen averaging radius. Once an averaging radiusand a filtering process is selected, an LES model can be developed and then solved numerically. One of the most interesting approaches to generate LES models is via approximatedeconvolution or approximate/asymptotic inverse of the filtering operator.Herein, we develop an abstract approach to modeling the motion of large eddies in aturbulent flow and postulate conditions on a general deconvolution operator that guaranteethe existence and uniqueness of strong solutions of Approximate Deconvolution Models. Wealso introduce new deconvolution operators which fit in this abstract theory. The Acceleratedvan Cittert algorithm and the Tikhonov regularization process are two methods for solvingill-posed problems that we adapt to turbulence. We study the mathematical properties ofthe resulting deconvolution operators.We also study a new family of turbulence models, the Leray-Tikhonov deconvolutionmodels, which is based on a modification (consistent with the large scales) of the Tikhonovregularization process. We perform rigorous numerical analysis of a computational attractivealgorithm for the considered family of models. Numerical experiments that support ourtheoretical results are presented.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Iuliana, Stanculescuius1@pitt.eduIUS1
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairLayton, William Jwjl@pitt.eduWJL
Committee MemberLennard, Christopher Jlennard@pitt.eduLENNARD
Committee MemberGaldi, Giovanni Pgaldi@engr.pitt.eduGALDI
Committee MemberYotov, Ivanyotov@math.pitt.eduYOTOV
Date: 3 November 2008
Date Type: Completion
Defense Date: 20 June 2008
Approval Date: 3 November 2008
Submission Date: 31 July 2008
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: Turbulence; Ill-posed problems; Large Eddy Simulation
Other ID:, etd-07312008-183023
Date Deposited: 10 Nov 2011 19:55
Last Modified: 15 Nov 2016 13:47


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