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Phenomenology and Computations of a Regularization of the Navier-Stokes Equations Related to a Non-Newtonian Fluid Flow Model

Hritz, Sara Marie (2010) Phenomenology and Computations of a Regularization of the Navier-Stokes Equations Related to a Non-Newtonian Fluid Flow Model. Master's Thesis, University of Pittsburgh. (Unpublished)

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Abstract

This paper analyzes the dynamics of non-Newtonian fluids, those whose viscosity is not constant. First, the Navier-Stokes equations are modified by introducing a new parameter with units of viscosity. Then, the energy equation and micro-scale of the model are derived. This allows the value of the parameter to be determined in order to make the micro-scale the order of the mesh width. Finally, the Finite Element Method with Backward Euler discretization is programmed using FreeFEM++ to simulate the model; a problem with known exact solution is used to test convergence of the method, and the step problem is also discussed.


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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Hritz, Sara Mariesaramhritz@gmail.com
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairLayton, Williamwjl@pitt.eduWJL
Committee MemberYotov, Ivanyotov@math.pitt.eduYOTOV
Committee MemberSussman, Myronsussmanm@math.pitt.eduMMS125
Date: 2 June 2010
Date Type: Completion
Defense Date: 22 April 2010
Approval Date: 2 June 2010
Submission Date: 23 April 2010
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Applied Mathematics
Degree: MS - Master of Science
Thesis Type: Master's Thesis
Refereed: Yes
Uncontrolled Keywords: partial differential equation; scientific computing
Other ID: http://etd.library.pitt.edu/ETD/available/etd-04232010-001758/, etd-04232010-001758
Date Deposited: 10 Nov 2011 19:41
Last Modified: 15 Nov 2016 13:42
URI: http://d-scholarship.pitt.edu/id/eprint/7575

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