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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
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1997
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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.
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Extent |
7766420 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-04-17
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Provider |
Vancouver : University of British Columbia Library
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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.
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DOI |
10.14288/1.0080530
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1997-11
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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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.