Phonon vortex dynamics in graphene ribbon by solving Boltzmann transport equation with ab initio scattering rates

In this work, we study thermal phonon vortex in graphene ribbon by a discrete-ordinate solution of phonon Boltzmann equation under Callaway's dual relaxation model. The phonon scattering rates of normal and resistive processes are acquired from ab initio calculation without need of any empirical input parameters. The temperature, size and isotope effects on transition from phonon vortex transport to conventional Fourier's heat conduction in both simple and complex geometries are investigated. The physical mechanism for the evolution of phonon vortex is declared by wide phonon mean free path distribution of resistive processes. A hierarchical vortex series is obtained with primary, secondary and terniary vortexes in a complicated geometry. The present work provides an accurate and efficient multi-scale numerical framework for modeling hydrodynamic phonon transport in high-thermal-conductivity materials and also sheds light on the heat dissipation applications.