Date of Award

5-2012

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Mathematical Science

Advisor

Lee, Hyesuk

Committee Member

Rebholz , Leo

Committee Member

Warner , Daniel

Abstract

In this thesis, we consider a viscoelastic flow in a moving domain, which has significant applications in biology and industry. Numerical approximation schemes are developed based on the Arbitrary Lagrangian-Eulerian (ALE) formulation of the flow equations. A spatial discretization is accomplished by the finite element method, and the time descritization is carried by either the implicit Euler method or the Crank-Nicolson method. Numerical results are presented for a fluid in a moving domain, where the boundary movement is specified by a given function. Then, we extend our work to a fluid-structure interaction problem. This system consists of a two-dimensional viscoelastic flow and a one-dimensional structure equation. We show how the system can be split and how each subproblem can be solved using interface conditions. Finally, we present some numerical results for the fluid-structure coupled system.

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.