The Gap-Tooth Method in Particle Simulations
Classical Physics
2009-11-10 v2 General Physics
Abstract
We explore the gap-tooth method for multiscale modeling of systems represented by microscopic physics-based simulators, when coarse-grained evolution equations are not available in closed form. A biased random walk particle simulation, motivated by the viscous Burgers equation, serves as an example. We construct macro-to-micro (lifting) and micro-to-macro (restriction) operators, and drive the coarse time-evolution by particle simulations in appropriately coupled microdomains (teeth) separated by large spatial gaps. A macroscopically interpolative mechanism for communication between the teeth at the particle level is introduced. The results demonstrate the feasibility of a closure-on-demand approach to solving hydrodynamics problems.
Cite
@article{arxiv.physics/0303010,
title = {The Gap-Tooth Method in Particle Simulations},
author = {C. William Gear and Ju Li and Ioannis G. Kevrekidis},
journal= {arXiv preprint arXiv:physics/0303010},
year = {2009}
}