<p>Phonon Boltzmann transport equation (BTE) is an important tool for studying the nanoscale thermal transport. Because phonons have a large spread in their properties, the non-gray phonon BTE is needed to accurately capture the nanoscale transport phenomena. However, due to the lack of accurate phonon properties as inputs and large computational costs of BTE solvers, the non-gray model is mainly used to qualitatively study nanoscale thermal transport phenomena. Recent advancements in first-principles calculations, nuetron scattering experiments, and MFP spectroscopy enable resolving accurate phonon properties for real materials. Such advancements make it possible to take the accurate phonon properties as inputs of BTE to achieve quantitative modeling of nanoscale thermal transport in real systems. At this stage, the large computational cost of non-gray BTE solvers is the remaining gap in quantitative modeling nanoscale thermal transport in real systems by non-gray phonon BTE. In the non-gray BTE solvers, the large spread in phonon properties is resolved by band discretization, which discretizes the phonon dispersion into a set of phonon bands. In each iteration of the solver, these bands are solved separately and then coupled through an energy conservation equation. The iterations end when all bands obey the BTE and energy conservation equation. As such, the computational cost of non-gray BTE solvers relates to the number of phonon bands, the computational cost of solving each phonon BTE, and the number of iterations. In this work, we comprehensively improve the efficiency of non-gray BTE solvers on unstructured meshes in these three aspects. Firstly, we reduce the number of phonon bands by proposing an improved band discretization scheme for real phonon properties based on the Gauss-Legendre quadrature. We find that the schemes used in previous studies require at least a few tens of bands for real phonon properties to ensure the accuracy. In contrast, using our scheme, the solution of phonon BTE converges (error &lt; 1%) with less than 10 phonon bands for typical materials. Secondly, we adopt a fast ﻿synthetic iterative scheme to reduce the number of iterations for BTE solvers on unstructured meshes. Previous studies used a local energy conservation equation to couple different phonon bands and require millions of iterations in the near-diffusive regime. In this scheme, a diffusion-type energy conservation equation is used to couple different phonon bands. Using this scheme, one only needs at most thousands of iterations for the entire ballistic-to-diffusive regime. Thirdly, we perform GPU parallelization for BTE solvers to speed up solving each phonon band. Compared with previous CPU parallelization, the GPU parallelization allows for larger acceleration rates for large-scale simulations. After these improvements, it is possible to perform large-scale BTE simulations for real materials.</p>

Efficiency Improvement in Solving Non-Gray Phonon Boltzmann Transport Equation

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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