Model dynamics on a multigrid across multiple length and time scales
Cellular Automata and Lattice Gases
2008-02-11 v1
Abstract
Most methods for modelling dynamics posit just two time scales: a fast and a slow scale. But many applications, including many in continuum mechanics, possess a wide variety of space-time scales; often they possess a continuum of space-time scales. I discuss an approach to modelling the discretised dynamics of advection and diffusion with rigorous support for changing the resolved spatial grid scale by just a factor of two. The mapping of dynamics from a finer grid to a coarser grid is then iterated to generate a hierarchy of models across a wide range of space-time scales, all with rigorous support across the whole hierarchy. This approach empowers us with great flexibility in modelling complex dynamics over multiple scales.
Keywords
Cite
@article{arxiv.0802.1098,
title = {Model dynamics on a multigrid across multiple length and time scales},
author = {A. J. Roberts},
journal= {arXiv preprint arXiv:0802.1098},
year = {2008}
}