An efficient multinomial sampling algorithm for spatially distributed stochastic particle simulations

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.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Jain, Rishabh K.

Contributors dc:contributor

• West, Matthew

• Multinomial sampling
• Stochastic matrix
• Particle Grid Method

Statement dc:rights

• Copyright 2011 Rishabh K. Jain

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/26200

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/26200