Predicting mesoscale spectral thermal conductivity using advanced deterministic phonon transport techniques

We present a review, demonstration, and simulation of phonon transport for the purposes of predicting materials performance at the mesoscale. We focus primarily on the development and implementation of a unified methodology to enable predictive heat transport. We report on the current state of the art as it pertains to deterministic phonon transport methodologies, discussing various topics concerning phonons. In application, we focus on the self-adjoint angular flux (SAAF) formulation of the Boltzmann transport equation for phonons, and develop the spatial, angular, and material property discretization required to accurately simulate the predictive physics of heat transport in dielectrics. We discuss thermal interfacial resistance and present our formulation of the diffuse mismatch model for simulating phonon interactions at internal boundaries. We recently developed a deterministic, spectral phonon transport method for predicting effective thermal conductivity (κ_eff), using Bose–Einstein source terms coupled through an average material temperature. This method provides a way of obtaining temperature using the linearized Boltzmann transport equation, without the necessary nonlinear outer iteration on temperature used in many approaches. Our thermal conductivity and heat flux results are consistent with existing research. We introduce a closure term to the phonon transport system which acts as a redistribution function for the total energy of the system and serves as an indicator of the amount of nonequilibrium behavior occurring in the system. We predict thermal conductivity and equilibrium temperature distributions in homogeneous and heterogeneous materials using data generated by ab initio density functional theory methods. We employ polarization, density of states and full dispersion spectra to resolve thermal conductivity with numerous angular and spatial discretizations. The equations associated with this method are solved via a modification of traditional source iteration. We compare the performance of source iteration applied to an existing uncoupled, traditional SAAF method to our new method and comment on the iterative performance of each. We observe ballistic and diffusive phonon scattering as acoustic thickness of the domain changes, and are able to make comparisons between the accuracy and efficiency of both methods.