Date of Award

8-2016

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

Committee Member

Dr. Hyesuk Lee, Committee Chair

Committee Member

Dr. Qingshan Chen

Committee Member

Dr. Vincent Ervin

Committee Member

Dr. Leo Rebholz

Abstract

In this work, we consider non-Newtonian fluid structure problems, which have 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 discretization is carried out by the implicit Euler method. We first consider a fluid-structure interaction problem that consists of a two-dimensional viscoelastic flow and a one-dimensional structure equation. We show how the system can be decoupled and how each subproblem can be solved using interface conditions. Numerical results of different algorithms are presented, showing the comparison between non-Newtonian and Newtonian fluids. We then extend the FSI problem into the 2D-2D case of a quasi-Newtonian fluid and a linear elastic structure. In this case, we present the stability and error estimation for both semi-discrete and fully discrete formulation. For the last part of this work, a 2D-2D viscoelastic FSI problem is considered with both monolithic algorithm and decoupled algorithm under Robin condition.

Included in

Mathematics Commons

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