Fast-Converging and Asymptotic-Preserving Simulation of Frequency Domain Thermoreflectance (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 phononBoltzmann equation, i.e., the Callaway’s model with dual relaxation times. Such akinetic system has two spatial Knudsen numbers related to the resistive and normalscatterings, and one temporal Knudsen number determined by the external oscillationfrequency. Thus, it is a challenge to develop an efficient numerical method. Here wefirst propose the general synthetic iterative scheme (GSIS) to solve the phonon Boltzmann equation, with the fast-converging and asymptotic-preserving properties: (i) thesolution 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 thebulk region is much larger than the phonon mean free path. Then, we investigate howthe heating frequency affects the heat conduction in different transport regimes.
Keywords: Frequency domain thermoreflectance; phonon Boltzmann equation; general synthetic iterative scheme.