  In this paper, a finite-volume discrete unified gas kinetic scheme (DUGKS)
based on the non-gray phonon transport model is developed for multiscale heat
transfer problem with arbitrary temperature difference. Under large temperature
difference, the phonon Boltzmann transport equation (BTE) is essentially
multiscale, not only in the frequency space, but also in the spatial space. In
order to realize the efficient coupling of the multiscale phonon transport, the
phonon scattering and advection are coupled together in the present scheme on
the reconstruction of the distribution function at the cell interface. The
Newtonian method is adopted to solve the nonlinear scattering term for the
update of the temperature at both the cell center and interface. In addition,
the energy at the cell center is updated by a macroscopic equation instead of
taking the moment of the distribution function, which enhances the numerical
conservation. Numerical results of the cross-plane heat transfer prove that the
present scheme can describe the multiscale heat transfer phenomena accurately
with arbitrary temperature difference in a wide range. In the diffusive regime,
even if the time step is larger than the relaxation time, the present scheme
can capture the transient thermal transport process accurately. Compared to
that under small temperature differences, as the temperature difference
increases, the variation of the temperature distribution behaves quite
differently and the average temperature in the domain increases in the
ballistic regime but decreases in the diffusive regime.
