A parabolic quadrilateral finite element for compressible and incompressible flows
Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1998.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2009
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| Online Access: | http://hdl.handle.net/1721.1/50060 |
| _version_ | 1811098223376334848 |
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| author | Hendriana, Dena |
| author2 | Klaus-Jürgen Bathe. |
| author_facet | Klaus-Jürgen Bathe. Hendriana, Dena |
| author_sort | Hendriana, Dena |
| collection | MIT |
| description | Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1998. |
| first_indexed | 2024-09-23T17:11:51Z |
| format | Thesis |
| id | mit-1721.1/50060 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T17:11:51Z |
| publishDate | 2009 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/500602020-08-24T13:48:21Z A parabolic quadrilateral finite element for compressible and incompressible flows Hendriana, Dena Klaus-Jürgen Bathe. Massachusetts Institute of Technology. Department of Mechanical Engineering Mechanical Engineering Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1998. Includes bibliographical references (leaves 156-161). A unified finite element solution scheme for incompressible and compressible flows would be most attractive in engineering practice. The objective in this thesis was to work toward this goal. A 9-node finite element for compressible and incompressible 2-D flow solutions is presented. In the compressible flow formulation, a new high-order derivative artificial diffusion and a new shock capturing term are employed to stabilize the formulation. The new upwinding term is shown numerically to stabilize the formulation and an inf-sup test is performed assuming idealized 1-D conditions. The new shock capturing term performed well in the solutions of various judiciously selected numerical examples. Various flow problems in which the Mach numbers range from about 0.0005 to 6 are considered. The numerical results indicate that the element is applicable to a wide range of analysis problems. For incompressible flows, the element must satisfy the relevant inf-sup condition, and an element is used with parabolic velocity and linear pressure interpolations (the 9/4c-element). An upwinding term in a similar form as for the compressible flow solution is introduced to stabilize the formulation. A convergence study with the formulation to estimate the order of convergence is performed. In addition, a new low order element is presented. The new solution schemes for compressible and incompressible flows provide effective solution techniques and the study provides insight into the difficulties encountered in the development of a unified scheme for incompressible and compressible flows. by Dena Hendriana. Sc.D. 2009-12-10T19:06:54Z 2009-12-10T19:06:54Z 1998 1998 Thesis http://hdl.handle.net/1721.1/50060 42191259 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 161 leaves application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mechanical Engineering Hendriana, Dena A parabolic quadrilateral finite element for compressible and incompressible flows |
| title | A parabolic quadrilateral finite element for compressible and incompressible flows |
| title_full | A parabolic quadrilateral finite element for compressible and incompressible flows |
| title_fullStr | A parabolic quadrilateral finite element for compressible and incompressible flows |
| title_full_unstemmed | A parabolic quadrilateral finite element for compressible and incompressible flows |
| title_short | A parabolic quadrilateral finite element for compressible and incompressible flows |
| title_sort | parabolic quadrilateral finite element for compressible and incompressible flows |
| topic | Mechanical Engineering |
| url | http://hdl.handle.net/1721.1/50060 |
| work_keys_str_mv | AT hendrianadena aparabolicquadrilateralfiniteelementforcompressibleandincompressibleflows AT hendrianadena parabolicquadrilateralfiniteelementforcompressibleandincompressibleflows |