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An efficient implicit kinetic scheme is developed to solve the stationaryphonon Boltzmann transport equation (BTE) based on the non-gray model includingthe phonon dispersion and polarization. Due to the wide range of the dispersedphonon mean free paths, the phonon transport under the non-gray model isessentially multiscale, and has to be solved differently and appropriately forvaried phonon frequencies and branches. The proposed implicit kinetic scheme iscomposed of a microscopic iteration and a macroscopic iteration. Themicroscopic iteration is capable of automatically adapting with varied phononmean free path of each phonon frequency and branch through solving the phononBTE. The energy transfer of all phonons is gathered together by the microscopiciteration to evaluate the heat flux. The temperature field is predicted througha macroscopic heat transfer equation according to the heat flux, and theequilibrium state in the phonon BTE is also updated. The combination of thephonon BTE solver and the macroscopic equation makes the present method veryefficient in a wide length scale. Three numerical tests, including thecross-plane, in-plane and nano-porous heat transfer in silicon, validate thatthe present scheme can handle with the phonon dispersion and polarizationcorrectly and predict the multiscale heat transfer phenomena efficiently in awide range. The present method could be tens of times faster than the typicalimplicit DOM and keeps the same amount of the memory requirements as theFourier solver for multiscale heat transfer problem.

An implicit kinetic scheme for multiscale heat transfer problem accounting for phonon dispersion and polarization