Review of multiscale simulation in submicron heat transfer

Over the last decade, interest in the simulation of micro- and nanoscale heat transfer has lead to the development of a variety of models and numerical methods for phonon transport in semiconductors and dielectrics. These models span direct simulation using molecular dynamics, a range of models of varying fidelity based on the Boltzmann transport equation, as well as simpler hyperbolic extensions to the classical Fourier heat conduction equation. The paper reviews the basics of phonon transport in crystals, available models for phonon transport, as well as numerical methods for solving the equations resulting from these models. Recommendations are made for future work.