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Mesoscopic numerical simulation has become an important tool in thermalmanagement and energy harvesting at the micro/nano scale, where the Fourier'slaw failed. However, it is not easy to efficiently solve the phonon Boltzmanntransport equation (BTE) from ballistic to diffusive limit. In order toaccelerate convergence, an implicit synthetic iterative scheme is developed forthe stationary phonon BTE, in which a macroscopic moment equation is invokedand solved iteratively coupled with the typical source iteration of the kineticequation. Different from previous numerical interpolation, the phonon BTE issolved again at the cell interface along the group velocity direction within acertain length when reconstructing the interfacial phonon distributionfunction. Fourier stability analysis shows that the present method couldconverge faster than the source iteration method in the (near) diffusiveregime. Numerical results prove that the present scheme can capture theballistic-diffusive effects correctly and efficiently. The present accelerationframework could be a powerful tool for simulating practical thermal engineeringproblems in the future.

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