Lattice Boltzmann scheme for hydrodynamic equation of phonon transport

In this work, a lattice Boltzmann scheme is developed for numerical solution of the phonon equation under Callaway's dual relaxation model in hydrodynamic limit. Through Chapman-Enskog expansion to with resistive scattering term as an equivalent source term, we recover which reduced Guyer-Krumhansl heat transport and Fourier's law limit dominant normal respectively. The transition from diffusive regime modeled extensively by present scheme, produces results good agreement benchmark solutions experimental measurement. Two well-known phenomena including Poiseuille flow second sound propagation are well captured scheme. This work will promote modeling deeper understanding non-Fourier induced scattering.