Development of a flow-condition-based interpolation 9-node element for incompressible flows
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2006.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2006
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| Online Access: | http://hdl.handle.net/1721.1/34642 |
| _version_ | 1826198074278543360 |
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| author | Banijamali, Bahareh |
| author2 | Klaus-Jürgen Bathe and Franz-Josef Ulm. |
| author_facet | Klaus-Jürgen Bathe and Franz-Josef Ulm. Banijamali, Bahareh |
| author_sort | Banijamali, Bahareh |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2006. |
| first_indexed | 2024-09-23T10:58:27Z |
| format | Thesis |
| id | mit-1721.1/34642 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T10:58:27Z |
| publishDate | 2006 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/346422019-04-11T00:56:07Z Development of a flow-condition-based interpolation 9-node element for incompressible flows Banijamali, Bahareh Klaus-Jürgen Bathe and Franz-Josef Ulm. Massachusetts Institute of Technology. Dept. of Civil and Environmental Engineering. Massachusetts Institute of Technology. Dept. of Civil and Environmental Engineering. Civil and Environmental Engineering. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2006. Includes bibliographical references. The Navier-Stokes equations are widely used for the analysis of incompressible laminar flows. If the Reynolds number is increased to certain values, oscillations appear in the finite element solution of the Navier-Stokes equations. In order to solve for high Reynolds number flows and avoid the oscillations, one technique is to use the flow condition-based interpolation scheme (FCBI), which is a hybrid of the finite element and the finite volume methods and introduces some upwinding into the laminar Navier-Stokes equations by using the exact solution of the advection-diffusion equation in the trial functions in the advection term. The previous works on the FCBI procedure include the development of a 4-node element and a 9-node element consisting of four 4-node sub-elements. In this thesis, the stability, the accuracy and the rate of convergence of the already published FCBI schemes is studied. In addition, a new FCBI 9-node element is proposed that obtains more accurate solutions than the earlier proposed FCBI elements. The new 9-node element does not obtain the solution as accurate as the Galerkin 9-node elements but the solution is stable for much higher Reynolds numbers (than the Galerkin 9-node elements), and accurate enough to be used to find the structural responses in fluid flow structural interaction problems. The Cubic-Interpolated Pseudo-particle (CIP) scheme is a very stable finite difference technique that can solve generalized hyperbolic equations with 3rd order accuracy in space. (cont.) In this thesis, in order to solve the Navier-Stokes equations, the CIP scheme is linked to the finite element method (CIP-FEM) and the FCBI scheme (CIP-FCBI). From the numerical results, the CIP-FEM and the CIP-FCBI methods appear to predict the solution more accurate than the traditional finite element method and t;he FCBI scheme. In order to obtain accurate solutions for high Reynolds number flows, we require a finer mesh for the finite element and the FCBI methods than for the CIP-FEM and the CIP-FCBI methods. Linking the CIP method to the finite element and the FCBI methods improves the accuracy for the velocities and the derivatives. In addition, when the flow is not at the steady state and the time dependent terms need to be included in the Navier-Stokes equations, or in the problems when the derivatives of the velocities need to be obtained to high accuracy, the CIP-FCBI method is more convenient than the FCBI scheme. by Bahareh Banijamali. Ph.D. 2006-11-07T16:44:25Z 2006-11-07T16:44:25Z 2006 2006 Thesis http://hdl.handle.net/1721.1/34642 70125009 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 167 leaves 6575290 bytes 6584738 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Civil and Environmental Engineering. Banijamali, Bahareh Development of a flow-condition-based interpolation 9-node element for incompressible flows |
| title | Development of a flow-condition-based interpolation 9-node element for incompressible flows |
| title_full | Development of a flow-condition-based interpolation 9-node element for incompressible flows |
| title_fullStr | Development of a flow-condition-based interpolation 9-node element for incompressible flows |
| title_full_unstemmed | Development of a flow-condition-based interpolation 9-node element for incompressible flows |
| title_short | Development of a flow-condition-based interpolation 9-node element for incompressible flows |
| title_sort | development of a flow condition based interpolation 9 node element for incompressible flows |
| topic | Civil and Environmental Engineering. |
| url | http://hdl.handle.net/1721.1/34642 |
| work_keys_str_mv | AT banijamalibahareh developmentofaflowconditionbasedinterpolation9nodeelementforincompressibleflows |