Acceleration strategy of source iteration method for the stationary phonon Boltzmann transport equation

Abstract

Mesoscopic numerical simulation has become an important tool in thermal management and energy harvesting at the micro/nano scale, where the Fourier's law failed. However, it is not easy to efficiently solve the phonon Boltzmann transport equation (BTE) from ballistic to diffusive limit. In order to accelerate convergence, an implicit synthetic iterative scheme is developed for the stationary phonon BTE, in which a macroscopic moment equation is invoked and solved iteratively coupled with the typical source iteration of the kinetic equation. Different from previous numerical interpolation, the phonon BTE is solved again at the cell interface along the group velocity direction within a certain length when reconstructing the interfacial phonon distribution function. Fourier stability analysis shows that the present method could converge faster than the source iteration method in the (near) diffusive regime. Numerical results prove that the present scheme can capture the ballistic-diffusive effects correctly and efficiently. The present acceleration framework could be a powerful tool for simulating practical thermal engineering problems in the future.