Date of Award

Spring 2014

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics and Statistics


Computational and Applied Mathematics

Committee Director

Yan Peng

Committee Member

Li-Shi Luo

Committee Member

Gordon Melrose

Committee Member

Shizhi Qian

Committee Member

Jin Wang


A description of the biomechanical character of red blood cells is given, along with an introduction to current computational schemes which use deformable capsules to simulate red blood cell shape change. A comprehensive two- and three-dimensional framework for the fluid-structure interaction between a deformable capsule and an ambient flow is provided. This framework is based on the immersed boundary method, using lattice Boltzmann and finite element methods for the fluid and structure, respectively. The characteristic response and recovery times of viscoelastic circular and spherical capsules are compared, and their dependence on simulation parameters is shown. The shape recovery of biconcave capsules in two and three dimensions is also considered, focusing on the role of simulation parameters and steady-state behaviour in two dimensions, while studying the capsule characteristics which lead to shape recovery and shape memory in three dimensions. Finally, the notion of interpreting membrane viscosity as an additional fluid viscosity is studied and a computational scheme based on power law fluids is described.