Title page for ETD etd-06062008-170423
|Type of Document
||Fithen, Robert Miller
||Adaptive finite element simulation of incompressible viscous flow
|Grossman, Bernard M.
|Reddy, Junuthula N.
|Cramer, Mark S.
|Henneke, Edmund G. II
|Ragab, Saad A.
|Date of Defense
A finite element method is employed for solving two- and three-dimensional
incompressible flows. The formulation is based on a segregated solution method.
In this segregated formulation, the velocities and pressures are uncoupled and the
equations for each are solved one after the other. This segregated solution method
is numerically compared to the penalty method and to previous reported data to
determine its validity. Next an iterative solution method which employs an element by -
element data structure of the finite element method is developed. Two types
of iterative methods are used. For a symmetric stiffness matrix, the conjugate
gradient method is used. For an unsymmetric stiffness matrix, the bi-conjugate
gradient method is used. Both iterative solution methods make use of a diagonal
preconditioning method (Jacobi preconditioning). Several problems are solved using
this segregated method. In two-dimensions, flow over a backward facing step and
flow in a cavity are investigated. In three-dimensions, the problems include flow
in a cavity at Reynolds number 100 and 1000, and flow in a curved duct. The
simulation compares very well with previously reported data, where available.
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