A fast synthetic iterative scheme for the stationary phonon Boltzmann transport equation

A fast iterative scheme for the linearized Boltzmann equation

Article history: Received 22 June 2016 Received in revised form 1 March 2017 Accepted 2 March 2017 Available online 7 March 2017

Boltzmann Solver for Phonon Transport

Boltzmann Transport Equation is solved numerically to model phonon transport in a subcontinuum domain in order to study heat transfer in thin film semiconductors. The phonon distribution function is modified to get an Energy equation from the Boltzmann Transport Equation. Gray form of the Energy equation is solved in the Relaxation time approximation to get the Phonon Energy Density distributio...

Solution of the Phonon Boltzmann Transport Equation Employing Rigorous Implementation of Phonon Conservation Rules

A finite volume scheme is developed to solve the phonon Boltzmann transport equation in an energy form accounting for phonon dispersion and polarization. The physical space and the first Brillouin zone are discretized into finite volumes and the phonon BTE is integrated over them. Second-order accurate differencing schemes are used for the discretization. The scattering term employs a rigorous ...

Thermal transport at the nanoscale: A Fourier's law vs. phonon Boltzmann equation study

Approach to equilibrium for the phonon Boltzmann equation

We study the asymptotics of solutions of the Boltzmann equation describing the kinetic limit of a lattice of classical interacting anharmonic oscillators. We prove that, if the initial condition is a small perturbation of an equilibrium state, and vanishes at infinity, the dynamics tends diffusively to equilibrium. The solution is the sum of a local equilibrium state, associated to conserved qu...