A hyperbolic lattice Boltzmann method for simulating non-Fourier heat conduction

Abstract

Classical lattice Boltzmann method (LBM) can recover Fourier's law. Since Fourier's law results in a parabolic heat conduction equation, the classical LBM is called the parabolic Boltzmann method (PLBM). But the Fourier’s law is based on the absurd assumption that the heat transfer rate is infinite, so whether the classical LBM can be used to observe the non-Fourier heat transfer problem remains controversial. In this paper, a hyperbolic lattice Boltzmann method (HLBM), which can be used to analyze the non-Fourier effect, was derived based on the Cattaneo-Vernotte (CV) model. To verify the accuracy of the HLBM, the process of a gold film irradiated by the laser was simulated using the HLBM and the PLBM and the results were compared with the experimental data. Because of the non-equilibrium heat transfer between electron and lattice during the laser irradiation, the two-step HLBM/PLBM models were proposed according to the two-temperature model. The results show that the electron temperatures simulated by the two models are not much different from each other, and both of them coincide with the experimental values. However, the thresholds obtained by the two models are different, and the results of HLBM are closer to the experimental values.