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.
| Identifer | oai:union.ndltd.org:PITT/oai:PITTETD:etd-04232010-001758 |
| Date | 02 June 2010 |
| Creators | Hritz, Sara Marie |
| Contributors | Myron Sussman, Ivan Yotov, William Layton |
| Publisher | University of Pittsburgh |
| Source Sets | University of Pittsburgh |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.library.pitt.edu/ETD/available/etd-04232010-001758/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to University of Pittsburgh or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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