Title page for ETD etd-06062008-170423

Type of Document Dissertation
Author Fithen, Robert Miller
URN etd-06062008-170423
Title Adaptive finite element simulation of incompressible viscous flow
Degree PhD
Department Engineering Mechanics
Advisory Committee
Advisor Name Title
Grossman, Bernard M. Committee Chair
Reddy, Junuthula N. Committee Chair
Cramer, Mark S. Committee Member
Henneke, Edmund G. II Committee Member
Ragab, Saad A. Committee Member
  • Viscous flow
Date of Defense 1993-08-05
Availability restricted

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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