Date of Award

5-2010

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Mathematical Science

Advisor

Rebholz, Leo G

Committee Member

Lee , Hyesuk K

Committee Member

Ervin , Vincent J

Abstract

This paper studies two artificial viscosity methods for approximating solutions to the Navier&ndashStokes Equations. Both methods that are introduced add stabilization, then remove it only on a coarse mesh. Both methods can be considered as conforming, mixed methods for 1) velocity and its gradient, and 2) velocity and vorticity. Herein we rigorously study the schemes both analytically and computationally, showing that both methods are unconditionally stable and optimally convergent. Numerical experiments show both methods provide improved results over the unstabilized Navier&ndashStokes Equations.

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