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Numerical prediction of multiscale heat transfer is a challenging problem dueto the wide range of time and length scales involved. In this work a discreteunified gas kinetic scheme (DUGKS) is developed for heat transfer in materialswith different acoustic thickness based on the phonon Boltzmann equation. Withdiscrete phonon direction, the Boltzmann equation is discretized with asecond-order finite-volume formulation, in which the time-step is fullydetermined by the Courant-Friedrichs-Lewy (CFL) condition. The scheme has theasymptotic preserving (AP) properties for both diffusive and ballistic regimes,and can present accurate solutions in the whole transition regime as well. TheDUGKS is a self-adaptive multiscale method for the capturing of local transportprocess. Numerical tests for both heat transfers with different Knudsen numbersare presented to validate the current method.

Phonon Boltzmann equation-based discrete unified gas kinetic scheme for multiscale heat transfer