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https://hdl.handle.net/2142/82347
Description
Title
Large Scale Simulations of Brownian Suspensions
Author(s)
Viera, Marc Nathaniel
Issue Date
2002
Doctoral Committee Chair(s)
Higdon, Jonathan J.L.
Department of Study
Chemical Engineering
Discipline
Chemical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Fluid and Plasma
Language
eng
Abstract
Our algorithm follows a Stokesian dynamics formulation by evaluating many-body hydrodynamic interactions using a far-field multipole expansion combined with a near-field lubrication correction. The breakthrough O(N ln N) scaling is obtained by employing a Particle-Mesh-Ewald (PME) approach whereby near-field interactions are evaluated directly and far-field interactions are evaluated using a grid based velocity computed with FFT's. This approach is readily extended to include the effects of Brownian motion. For interacting particles, the fluctuation-dissipation theorem requires that the individual Brownian forces satisfy a correlation based on the N body resistance tensor R. The accurate modeling of these forces requires the computation of a matrix square root R 1/2 for matrices up to order 2 x 105. The cost of this operation via direct methods would be prohibitive and would completely overwhelm the computational cost of the Stokesian dynamics calculation. We have developed a novel iterative approach which exploits the Particle-Mesh-Ewald formulation to perform this calculation.
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