Deviational methods for small-scale phonon transport

Abstract

We review deviational methods for solving the Boltzmann equation governing phonon transport processes in the context of small-scale, solid-state heat transfer. We briefly discuss the numerical foundations of deviational algorithms as well as basic simulation methodology. Particular emphasis is given to recent developments in the field yielding appreciable efficiency improvements, such as linearized and adjoint formulations, and their applications to complex multiscale problems. Recently developed methods for simulating the ab initio collision operator for applications to phonon transport in novel two-dimensional materials, such as graphene, are also reviewed and discussed.