Open Collections

UBC Theses and Dissertations

UBC Theses Logo
Featured Collection

UBC Theses and Dissertations

Analysis and computation of immersed boundaries, with application to pulp fibres Stockie, John Michael

Abstract

Immersed fibres are a very useful tool for modeling moving, elastic interfaces that interact with a surrounding fluid. The Immersed Boundary Method is a computational tool based on the immersed fibre model which has been used successfully to study a wide range of applications including blood flow in the heart and arteries and motion of suspended particles. This work centres around a linear analysis of an isolated fibre in two dimensions, which pinpoints a discrete set of solution modes associated solely with the fibre. We investigate the stability and stiffness characteristics of the fibre modes and then relate the results to the severe time step restrictions experienced in explicit and semi-implicit immersed boundary computations. A subset of the modes corresponding to tangential oscillations of the fibre are the main source of stiffness, which intensifies when the fibre force is increased or fluid viscosity is decreased — this explains why computations are limited to unrealistically small Reynolds numbers. We also investigate the effects of smoothing the fibre over a given thickness, which corresponds to the delta function approximation that is central to the discrete scheme. The results can be applied to explore the accuracy of various interpolation methods in an idealised setting. The analysis is next extended to predict time step restrictions and convergence rates for various explicit and semi-implicit discretisations. The results are verified in numerical experiments. Finally, we introduce a novel application of the Immersed Boundary Method to the motion of pulp fibres in a two-dimensional shear flow. The method is shown to reproduce both theoretical results and experimentally observed behaviour over a wide range of parameter values.

Item Metadata

Title
Analysis and computation of immersed boundaries, with application to pulp fibres
Creator
Stockie, John Michael
Publisher
University of British Columbia
Date Issued
1997
Description
Immersed fibres are a very useful tool for modeling moving, elastic interfaces that interact with a surrounding fluid. The Immersed Boundary Method is a computational tool based on the immersed fibre model which has been used successfully to study a wide range of applications including blood flow in the heart and arteries and motion of suspended particles. This work centres around a linear analysis of an isolated fibre in two dimensions, which pinpoints a discrete set of solution modes associated solely with the fibre. We investigate the stability and stiffness characteristics of the fibre modes and then relate the results to the severe time step restrictions experienced in explicit and semi-implicit immersed boundary computations. A subset of the modes corresponding to tangential oscillations of the fibre are the main source of stiffness, which intensifies when the fibre force is increased or fluid viscosity is decreased — this explains why computations are limited to unrealistically small Reynolds numbers. We also investigate the effects of smoothing the fibre over a given thickness, which corresponds to the delta function approximation that is central to the discrete scheme. The results can be applied to explore the accuracy of various interpolation methods in an idealised setting. The analysis is next extended to predict time step restrictions and convergence rates for various explicit and semi-implicit discretisations. The results are verified in numerical experiments. Finally, we introduce a novel application of the Immersed Boundary Method to the motion of pulp fibres in a two-dimensional shear flow. The method is shown to reproduce both theoretical results and experimentally observed behaviour over a wide range of parameter values.
Extent
7766420 bytes
Genre
Thesis/Dissertation
Type
Text
File Format
application/pdf
Language
eng
Date Available
2009-04-17
Provider
Vancouver : University of British Columbia Library
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
DOI
10.14288/1.0080530
URI
http://hdl.handle.net/2429/7346
Degree
Doctor of Philosophy - PhD
Program
Mathematics
Affiliation
Science, Faculty of; Mathematics, Department of
Degree Grantor
University of British Columbia
Graduation Date
1997-11
Campus
UBCV
Scholarly Level
Graduate
Aggregated Source Repository
DSpace

Item Media

Item Citations and Data

Rights

For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.