A finite volume scheme is developed to solve the phonon Boltzmann transport equation in an energy form accounting for phonon dispersion and polarization. The physical space and the first Brillouin zone are discretized into finite volumes and the phonon BTE is integrated over them. Second-order accurate differencing schemes are used for the discretization. The scattering term employs a rigorous implementation of phonon momentum and energy conservation laws in determining the rate of normal and Umklapp processes. The method is applied to a variety of bulk silicon and silicon thin-film conduction problems and shown to perform satisfactorily.
Solution of the Phonon Boltzmann Transport Equation Employing Rigorous Implementation of Phonon Conservation Rules
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Wang, T, & Murthy, JY. "Solution of the Phonon Boltzmann Transport Equation Employing Rigorous Implementation of Phonon Conservation Rules." Proceedings of the ASME 2006 International Mechanical Engineering Congress and Exposition. Heat Transfer, Volume 3. Chicago, Illinois, USA. November 5–10, 2006. pp. 463-471. ASME. https://doi.org/10.1115/IMECE2006-14090
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