We consider the usage of higher order spectral element methods for the solution of
problems in structures and fluid mechanics areas. In structures applications we study
different beam theories, with mixed and displacement based formulations, consider
the analysis of plates subject to external loadings, and large deformation analysis of
beams with continuum based formulations. Higher order methods alleviate the problems
of locking that have plagued finite element method applications to structures, and also
provide for spectral accuracy of the solutions. For applications in computational fluid
dynamics areas we consider the driven cavity problem with least squares based finite element
methods. In the context of higher order methods, efficient techniques need to be devised for the solution of the resulting algebraic systems of equations and we explore the usage of element by element bi-orthogonal conjugate gradient solvers for solving
problems effectively along with domain decomposition algorithms for fluid problems. In
the context of least squares finite element methods we also explore the usage of Multigrid
techniques to obtain faster convergence of the the solutions for the problems of interest.
Applications of the traditional Lagrange based finite element methods with the Penalty finite
element method are presented for modelling porous media flow problems. Finally, we explore
applications to some CFD problems namely, the flow past a cylinder and forward facing
step.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2010-05-7647 |
| Date | 2010 May 1900 |
| Creators | Ranjan, Rakesh |
| Contributors | Reddy, J.N. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | thesis, text |
| Format | application/pdf |
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