Development of a flow-condition-based interpolation 9-node element for incompressible flows

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Civil and Environmental Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Banijamali, Bahareh

Advisor dc:contributor.advisor

• Klaus-Jürgen Bathe and Franz-Josef Ulm.

• Civil and Environmental Engineering.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/34642

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/34642