An efficient multinomial sampling algorithm for spatially distributed stochastic particle simulations
Jain, Rishabh K.
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https://hdl.handle.net/2142/26200
Description
Title
An efficient multinomial sampling algorithm for spatially distributed stochastic particle simulations
Author(s)
Jain, Rishabh K.
Issue Date
2011-08-25T22:18:28Z
Director of Research (if dissertation) or Advisor (if thesis)
West, Matthew
Department of Study
Mechanical Sci & Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Multinomial sampling
Stochastic matrix
Particle Grid Method
Abstract
This study develops a new particle-resolved method (PGM) for stochastically simulating the transport of particles by advection and diffusion processes. This particle-resolved method is based on a multinomial sampling algorithm which calculates the number of particles transferred between adjacent sub-volumes in the domain at each time-step. The particle-resolved method is compared with the traditional finite volume and Monte Carlo methods. Stability and convergence of the particle method are also investigated. We extend the particle grid method (PGM) to the large time-step particle grid method (LTPGM) which allows us to use bigger time-steps even when the grid is made finer. Errors between different methods have been rigorously derived. Results from the numerical simulations have been shown to confirm the mathematically derived results.
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