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We present a new method for predicting effective thermal conductivity($\kappa_{\textrm{eff}}$) in materials, informed by ${ab\,initio}$ materialproperty simulations. Using the Boltzmann transport equation in a Self-AdjointAngular Flux formulation, we performed simulations in silicon at roomtemperatures over length scales varying from 10 nm to 10 $\mu$m and reporttemperature distributions, spectral heat flux and thermal conductivity. Ourimplementation utilizes a Richardson iteration on a modified version of thephonon scattering source. In this method, a closure term is introduced to thetransport equation which acts as a redistribution kernel for the total energybath of the system. This term is an effective indicator of the degree ofdisorder between the spectral phonon radiance and the angular phonon intensityof the transport system. We employ polarization, density of states and fulldispersion spectra to resolve thermal conductivity with numerous angular andspatial discretizations.

Prediction of thermal conductivity in dielectrics using fast, spectrally-resolved phonon transport simulations