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Mathematical Architecture for Models of Fluid Flow Phenomena

Labovschii, Alexandr (2008) Mathematical Architecture for Models of Fluid Flow Phenomena. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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This thesis is a study of several high accuracy numerical methods for fluid flow problems and turbulence modeling.First we consider a stabilized finite element method for the Navier-Stokes equations which has second order temporal accuracy. The method requires only the solution of one linear system (arising from an Oseen problem) per time step. We proceed by introducing a family of defect correction methods for the time dependent Navier-Stokes equations, aiming at higher Reynolds' number. The method presented is unconditionally stable, computationally cheap and gives an accurate approximation to the quantities sought. Next, we present a defect correction method with increased time accuracy. The method is applied to the evolutionary transport problem, it is proven to be unconditionally stable, and the desired time accuracy is attained with no extra computational cost. We then turn to the turbulence modeling in coupled Navier-Stokes systems - namely, MagnetoHydroDynamics. Magnetically conducting fluids arise in important applications including plasma physics, geophysics and astronomy. In many of these, turbulent MHD (magnetohydrodynamic) flows are typical. The difficulties of accurately modeling and simulating turbulent flows are magnified many times over in the MHD case. We consider the mathematical properties of a model for the simulation of the large eddies in turbulent viscous, incompressible, electrically conducting flows. We prove existence, uniqueness and convergence of solutions for the simplest closed MHD model. Furthermore, we show that the model preserves the properties of the 3D MHD equations. Lastly, we consider the family of approximate deconvolution models (ADM) for turbulent MHD flows. We prove existence, uniqueness and convergence of solutions, and derive a bound on the modeling error. We verify the physical properties of the models and provide the results of the computational tests.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Labovschii, Alexandrayl2@pitt.eduAYL2
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairLayton, William Jwjl@pitt.eduWJL
Committee MemberRiviere,
Committee MemberTrenchea, Catalintrenchea@pitt.eduTRENCHEA
Committee MemberGaldi, Giovanni Pgaldi@engr.pitt.eduGALDI
Committee MemberYotov, Ivanyotov@math.pitt.eduYOTOV
Committee MemberSussman,
Date: 30 October 2008
Date Type: Completion
Defense Date: 2 May 2008
Approval Date: 30 October 2008
Submission Date: 10 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: deconvolution; MagnetoHydroDynamics; subgrid scaling; turbulence; defect correction; LES
Other ID:, etd-07102008-083457
Date Deposited: 10 Nov 2011 19:50
Last Modified: 15 Nov 2016 13:45


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