2026-09-19T18:59:27Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/26200 2023-07-10 col_2142_5131 col_2142_14787 com_2142_5130 com_2142_9630 com_2142_234

West, Matthew Jain, Rishabh K. 2011-08-25T22:18:28Z 2011-08-25T22:18:28Z 2011-08-25T22:18:28Z 2011-08 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. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2011-07-16T15:24:16Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Jain_Rishabh.pdf: 442156 bytes, checksum: 4660a035eed3b4c17c1f84383d75f610 (MD5) Made available in DSpace on 2011-08-25T22:18:28Z (GMT). No. of bitstreams: 2 Jain_Rishabh.pdf: 442156 bytes, checksum: 4660a035eed3b4c17c1f84383d75f610 (MD5) license.txt: 4060 bytes, checksum: a443257a8a4cb12d99d463b2cbf5babb (MD5) http://hdl.handle.net/2142/26200 en Copyright 2011 Rishabh K. Jain Multinomial sampling Stochastic matrix Particle Grid Method An efficient multinomial sampling algorithm for spatially distributed stochastic particle simulations Mechanical Sci & Engineering 1917 Mechanical Engineering 0133 University of Illinois at Urbana-Champaign Thesis M.S. MS:Mechanical Engineerng -UIUC 10KS0133MS