Atomistic-to-Continuum Coupling Methods for Heat Transfer in Solids

At very small scales, many continuum thermal and mechanical models lose applicability as the effects of surfaces, grain boundaries, defects, and other deviations from a perfect continuum become important. In fact, ordinary continuum concepts like stress, strain, and temperature may be difficult to define at the atomic scale. Atomistic simulation techniques like molecular dynamics provide a way to simulate these small-scale behaviors, but computational cost limits the time and length scales accessible by these computations. Coupled atomistic-to-continuum simulation techniques have been developed to combine the strengths of these two modeling approaches. We review recently introduced methods to allow two-way exchange of thermal information in dynamically coupled simulations, linking a continuum temperature field to atomic vibrations. Techniques are presented that conserve the total thermal energy of coupled systems, allow convenient application of thermal boundary conditions in terms of continuum temperature and heat flux, and capture the electron temperature field that is important in metals and semiconductors. Example problems and applications demonstrate the effectiveness of these methods. This edition first published 2013