Model dynamics on a multigrid across multiple length and time scales. 29p.

Abstract

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. The computer algebra described here empowers an approach to modelling the dynamics of advection and diffusion with rigorous support for changing the resolved space-time scale by just a factor of two. The mapping of dynamics from a finer grid to a coarser grid may be iterated to generate a hierarchy of models across a wide range of space-time scales.