论文标题
晶格玻尔兹曼（用于声子传输的流体动力方程式）
Lattice Boltzmann scheme for hydrodynamic equation of phonon transport
论文作者
论文摘要
在这项工作中，在Callaway的双重弛豫模型下开发了一个晶格Boltzmann方案，用于在流体动力极限下的数值解。通过Chapman-Enskog扩展到晶格Boltzmann方程，电阻散射项为等效源项，我们恢复了一个声子流体动力方程式，该方程还原为Guyer-Krumhansl热传输方程，并在较大的正常散射和优势散射的极限上恢复了傅立叶的定律。从扩散状态到流体动力学制度的几种热传输病例是通过当前的数值方案进行广泛建模的，这与基准溶液产生了良好的一致性。晶格Boltzmann方案很好地捕获了两个众所周知的声子流体动力现象，包括声子Poiseuille流和第二个声音传播。这项工作将促进对声子正常散射引起的非峰热传输的数值建模和更深入的了解。
In this work, a lattice Boltzmann scheme is developed for numerical solution of the phonon Boltzmann equation under Callaway's dual relaxation model in the hydrodynamic limit. Through a Chapman-Enskog expansion to the lattice Boltzmann equation with the resistive scattering term as an equivalent source term, we recover a phonon hydrodynamic equation which is reduced to the Guyer-Krumhansl heat transport equation and the Fourier's law in the limit of dominant normal scattering and dominant resistive scattering respectively. Several cases of heat transport from diffusive regime to hydrodynamic regime are modeled extensively by the present numerical scheme, which produces results in good agreement with the benchmark solutions. Two well-known phonon hydrodynamic phenomena including the phonon Poiseuille flow and second sound propagation are well captured by the lattice Boltzmann scheme. This work will promote the numerical modeling and deeper understanding of the non-Fourier heat transport induced by phonon normal scattering.
