Abstract

Multi-scale simulations are becoming increasingly more important in the field of computational modelling. There has been considerable progress in developing coupled models which include both quantum mechanical atomistic simulations and classical molecular dynamics (using empirical inter-atomic potentials). However, many real world problems require the resolution of lengths and timescales far beyond the largest possible quantum/molecular dynamics simulation. Therefore, a further level of coarse graining is often required, linking the molecular system to a continuum based model in order to capture the effects of the surrounding environment.

This continuum-discrete-quantum coupling approach has been successfully employed already and can be seen (for example) in the modelling of crack tip propagation in solids. The aim of this talk is to introduce some of the challenges and developments in continuum-molecular coupling for the case of computational fluid dynamics. This presents a number of additional challenges due to the time evolution of the fluid and the differences in reference frame between the descriptions. A mathematical operator framework is introduced to express both systems in an equivalent manner, building on the statistical mechanical framework of Irving and Kirkwood (1950). The use of Hamilton’s principle for coupling is also discussed and the required techniques are outlined for the computational implementation of coupled simulation on multi-core architectures. The talk will conclude with a discussion of this work as part of the long term aim to develop multi-scale simulation tools. The aim is to accurately model fluid solid interactions at the nano-scale while resolving length scales of engineering importance.