Direct Simulation of the Nonlinear Boltzmann Transport Equation for Phonons

In order to solve a Boltzmann transport equation (BTE) of phonons for investigating heat conduction in non-metallic solids, we propose to employ a DSMC (direct simulation Monte Carlo) scheme to simulate dynamics of phonons in analogy with rarefied gas. In this paper, we describe the DSMC scheme for phonon dynamics and present some results with our prototype codes for a face-centered cubic model. The dynamics of phonons with two branches of acoustic modes is discussed, in the case where the distribution of phonons in strong nonequilibrium situation is driven into equilibrium.