  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.

Computational Physics