Discontinuous Galerkin finite element method for phonon Boltzmann transport equation under Callaway's scattering model

Spatially and temporally dependent solutions of phonon Boltzmann transport equation(BTE) are essential to investigate thermal transport in finite-size micro- and nano-scale devices. This study focuses on the development of a numerical framework tailored for addressing the phonon BTE within irregular geometries. Specifically, a two-dimensional implicit nodal discontinuous Galerkin finite element method (DGFEM) is developed for solving the phonon BTE with Callaway's dual relaxation approximation. Through this methodology, the size and wave effects of thermal transport in graphene ribbons with varying geometries are investigated. Numerical simulations conducted using the proposed DGFEM exhibit commendable concordance with extant literature, affirming the method's efficacy and precision in modeling phonon transport within finite-size microstructures. Furthermore, the application of DGFEM facilitates an exploration of thermal transport in kinked graphene ribbons. Notably, in exceedingly narrow graphene ribbons, the introduction of kinks results in a significant reduction of thermal conductance by up to 14.8 %. Moreover, the presence of kinks elicits a discernible monotonic escalation of thermal conductance with temperature. These findings furnish tangible directives for manipulating thermal transport in microstructures via kink modulation.