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Direction-Splitting Schemes For Particulate Flows Open Access


Other title
direct numerical simulation
boundary fitting
fluidized bed
particulate flow
parallel computing
collision modelling
Incompressible flow
implicit scheme
second order accurate
direction splitting
Navier Stokes
Type of item
Degree grantor
University of Alberta
Author or creator
Keating, John William
Supervisor and department
Minev, Peter (Mathematics)
Bowman, John (Mathematics)
Examining committee member and department
Bowman, John (Mathematics)
Yu, Xinwei (Mathematics)
Minev, Peter (Mathematics)
van Roessel, Henry (Mathematics)
Stockie, John (Mathematics)
Flynn, Morris (Mechanical Engineering)
Department of Mathematical and Statistical Sciences
Applied Mathematics
Date accepted
Graduation date
Doctor of Philosophy
Degree level
This thesis introduces a new temporally second-order accurate direction-splitting scheme for implicitly solving parabolic or elliptic partial differential equations in complex-shaped domains. While some other splitting schemes can be unstable in such domains, numerical evidence suggests that the new splitting scheme is unconditionally stable even when using non-commutative spatial operators. The new direction-splitting scheme is combined with other splitting schemes to produce an efficient numerical method for solving the incompressible Navier-Stokes equations. Finite differences using staggered grids and sharp boundary-fitting is used to achieve second-order spatial accuracy. The numerical method is extended to perform direct numerical simulations of particulate flows where each rigid particle is used as Dirichlet boundary conditions for the Navier-Stokes equations, and forces on each particle are computed by performing surface integrals of the fluid stress. The method is validated by reproducing experimental results, reproducing numerical results of other independent authors, and demonstrating second-order convergence on manufactured solutions. Particle collisions are handled using a dry viscoelastic soft-sphere model with sub-time stepping. An additional model based on lubrication theory is proposed and shown to agree with experiments of submerged collisions. The complete numerical method is suitable for parallel computing. Weak scaling results of a 3D fluidized bed simulation containing two million particles suggests that flows containing one billion particles could be computed on today's supercomputers.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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