TY - JOUR
T1 - Fast-Converging and Asymptotic-Preserving Simulation of Frequency Domain Thermoreflectance
AU - Liu , Jia
AU - Wu , Lei
JO - Communications in Computational Physics
VL - 1
SP - 65
EP - 93
PY - 2023
DA - 2023/08
SN - 34
DO - http://doi.org/ 10.4208/cicp.OA-2023-0053
UR - https://global-sci.org/intro/article_detail/cicp/21880.html
KW - Frequency domain thermoreflectance, phonon Boltzmann equation, general synthetic iterative scheme.
AB - <p style="text-align: justify;">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.</p>