A Monte Carlo scheme for tracking filling fronts

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A Monte Carlo (MC) scheme for tracking filling fronts is developed. The test problem of tracking fluid injected into a thin mold is considered. The MC scheme iteratively redistributes the volume entering the mold among the cells of a spatial discretization. The transition probabilities used in the MC scheme, which determine how the fluid volume is redistributed, are derived from a discrete representation of the governing steady-state pressure equation. Analysis shows that the MC steps are equivalent to an iterative solution of the discrete equations. Further, it is shown that the MC scheme can be reconfigured into the form of a standard Lattice Boltzmann Method (LBM). Results show that the proposed MC scheme is accurate, does not require an explicit field calculation of the fluid pressure field, and, when compared with existing numerical filling algorithms, exhibits computation times over 1000 times faster.

Original languageEnglish (US)
Pages (from-to)399-411
Number of pages13
JournalJournal of Computational Physics
Issue number2
StatePublished - Nov 1 2004

Bibliographical note

Funding Information:
This work was supported by the STC program of the National Science Foundation via the National Center for Earth-surface Dynamics under the agreement Number EAR- 0120914. The author would like to acknowledge extensive discussions with his colleagues in the NCED working group on Integration Across Scales.

Copyright 2019 Elsevier B.V., All rights reserved.


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