Committee Chair

Wang, Jin

Committee Member

Cox, Christopher L. (Christopher Lee); Barioli, Francesco; Liang, Yu

Department

Dept. of Mathematics

College

College of Engineering and Computer Science

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

This dissertation is concerned with the modeling, simulation, and analysis of moving interface problems involving viscous fluids and solid structures. The main computational technique employed in this work is the immersed boundary method, a widely known numerical method for fluid-structure interaction (FSI). In this technique, the fluid equations are solved in an Eulerian grid and the structure is treated as a network of Lagrangian nodes. The communication between the fluid and structure dynamics is established by the use of the Dirac delta function. Utilizing the immersed boundary method, we have studied three biophysical applications. In the first application, we computed the interaction between microtubules and cytoplasmic flow in plant cells. We found that such interaction plays an important role in the assembly and orientation of microtubules. We also validated the simulation results through a comparison with experimental measurements. The second application involved the response of a polymeric material to an oscillatory shear flow. We considered three weave topologies of polymers in 3D: (i) vertically aligned; (ii) orthogonal; and (iii) orthogonal and interlaced. We conducted a detailed FSI computational study to reveal the impact of fluid dynamics on the material and topological properties of polymers. In the third application, we investigated the dynamics of microfibrils in the primary cell walls of plants that contain mainly pectin, a gel-like fluid, and a small amount of water. The interaction between microfibrils, pectin and water constitute a problem of coupled fluid-structure interaction and two-phase flow, which is numerically solved by integrating the immersed boundary method and the volume of fluid (VOF) method.

Degree

Ph. D.; A dissertation submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Doctor of Philosophy.

Date

8-2024

Subject

Computational fluid dynamics; Fluid dynamics--Mathematical models

Keyword

immersed boundary method; volume of fluid method; microtubules; polymeric material; oscillatory shear; microfibrils

Discipline

Numerical Analysis and Computation

Document Type

Doctoral dissertations

DCMI Type

Text

Extent

xiv, 104 leaves

Language

English

Rights

http://rightsstatements.org/vocab/InC/1.0/

License

http://creativecommons.org/licenses/by/3.0/

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