(untitled) (Communications in Computational Physics, 2023)
The heat conduction under fast external excitation exists in many experiments measuring the thermal conductivity in solids, which is described by the phonon Boltzmann equation, i.e., the Callaway’s model with dual relaxation times. Such a kinetic system has two spatial Knudsen numbers related to the resistive and normal scatterings, and one temporal Knudsen number determined by the external oscillation frequency. Thus, it is a challenge to develop an efficient numerical method. Here we first propose the general synthetic iterative scheme (GSIS) to solve the phonon Boltzmann equation, with the fast-converging and asymptotic-preserving properties: (i) the solution can be found within dozens of iterations for a wide range of Knudsen numbers and frequencies, and (ii) the solution is accurate when the spatial cell size in the bulk region is much larger than the phonon mean free path. Then, we investigate how the heating frequency affects the heat conduction in different transport regimes.