A discrete unified gas kinetic scheme for phonon Boltzmann transport equation accounting for phonon dispersion and polarization

Abstract

Different from the gray model for phonon transport, the non-gray model takes account of the dispersion and polarization of phonons. Under the consideration of the real dispersion curve, the phonon transport in micro and nanoscale devices is intractable multiscale problem. On the basis of previous work about gray model for phonon transport by a discrete unified gas kinetic scheme (DUGKS), we extend the DUGKS to solving non-gray transport determined by the frequency-dependent phonon Boltzmann equation. The extension is straightforward due to the intrinsic multiscale property of the DUGKS. Four classic test cases, cross-plane heat conduction, in-plane heat conduction, one-dimensional transient thermal grating problem and two-dimensional steady phonon conduction are used to validate our scheme. Numerical results show that the present scheme can accurately capture ballistic-diffusive transport phenomenon in a wide range. This method may provide a powerful numerical tool for a deep research into nanoscale and microscale heat transport.