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. The transition of heat transport from diffusive regime to hydrodynamic regime is modeled extensively by the present numerical scheme, which produces results in good agreement with the benchmark solutions and experimental measurement. 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.

在这项工作中，开发了一种格子玻尔兹曼方案，用于在流体动力学极限下卡拉威的双重弛豫模型下声子玻尔兹曼方程的数值解。通过以电阻散射项作为等效源项对晶格 Boltzmann 方程的 Chapman-Enskog 展开，我们恢复了一个声子流体动力学方程，该方程简化为 Guyer-Krumhansl 热传输方程和在主导法向散射极限下的傅立叶定律和主要电阻散射。本数值方案广泛模拟了从扩散状态到流体动力学状态的热传输的转变，其产生的结果与基准解和实验测量非常一致。两种众所周知的声子流体动力学现象，包括声子泊肃叶流和第二声传播，都被格子玻尔兹曼方案很好地捕捉到了。这项工作将促进对声子法向散射引起的非傅立叶热传输的数值建模和更深入的理解。