Effect of discrete number of velocity directions of phonon on thermal conductivity prediction in the cross-plane direction of superlattices

In this paper, we analyze the effect of the discrete number of velocity directions of the phonon on thermal conductivity prediction in the cross-plane direction of superlattices based on solving the phonon Boltzmann transport equation (BTE) numerically. The simulation shows that the accuracy of the calculation is mainly affected by discretization number of polar angle (Nθ). To improve the efficiency in the two-dimensional situation, choosing a proper discrete number of velocity directions of the phonon can be used. Besides, the relationship between the control angle (M) and Knudsen (Kn) number is concluded when the relative error is less than 5%.