Phonon hydrodynamics: Progress, applications and perspectives

Phonon hydrodynamics is an effective macroscopic method to study heat transport in dielectric solid, which has a clear and intuitive physical picture, and also an elegant and unified mathematical description. The present work provides a systematic summary of its theoretical foundation, historical line, recent progress and applications. The historical line of phonon hydrodynamics consists of three stages in all: the classical phonon hydrodynamics, phenomenological phonon hydrodynamics and generalized phonon hydrodynamics. The unified kinetic theory framework for classical phonon hydrodynamics is first elaborated, with an incorporation of various previous phonon hydrodynamic equations valid in different situations through a Chapman-Ensokg expansion solution to phonon Boltzmann equation. The main idea and content of phenomenological phonon hydrodynamics is then summarized, together with its application in nanoscale heat transport. Its historical logic and limitation is therefore elucidated along the classical phonon hydrodynamics. Meanwhile, to foster the wide applications of phonon hydrodynamics in complex systems, we give an introduction to the recent advance of corresponding numerical schemes, including both phonon lattice Boltzmann method and phonon Monte Carlo method. Finally, the perspectives of phonon hydrodynamics are discussed towards a more accurate description of heat transport in nanosystems. The generalized phonon hydrodynamics is interpreted in terms of its connotation and denotation, as well as the nonequilibrium thermodynamic foundation. The present work aims at promoting the further development of phonon hydrodynamics and its application in uncovering the mechanisms of heat transport in extreme situations.