Graduation Semester and Year

2010

Language

English

Document Type

Thesis

Degree Name

Master of Science in Aerospace Engineering

Department

Mechanical and Aerospace Engineering

First Advisor

Brian Dennis

Abstract

The finite element method has become a popular method for the solution of the incompressible Navier-Stokes equations. High Reynolds number cases require fine meshes so computational efficiency becomes an important factor in algorithm and code development. In this work, a Galerkin finite element method is proposed to solve the two dimensional incompressible Navier-Stokes equations. This approach typically leads to a sparse and indefinite matrix that is difficult to solve efficiently. The formation of an indefinite matrix is avoided in the present work by introducing an artificial compressibility term in the continuity equation. The concept of this method is to transform the elliptic incompressible equation to the hyperbolic type compressible system which can be solved by standard implicit or explicit time-marching methods. The primitive variables are used for flow properties. The method features unequal order interpolation for the velocity variables and pressure. The Taylor Galerkin formulation is introduced as a stabilization procedure to eliminate the numerical oscillations that occur in convection dominated flows. The Newton-Raphson method is used to resolve the non-linearity at each time step. In order to test the method, a finite element code was developed for triangular meshes. The code was applied to the standard lid driven cavity problem. The numerical results were compared with benchmark results from the literature

Disciplines

Aerospace Engineering | Engineering | Mechanical Engineering

Comments

Degree granted by The University of Texas at Arlington

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