This paper presents a new numerical scheme for simulating multidimensional transient and steady-state microscale energy transport. The new method is based on the method of characteristics that follows heat carriers along their pathline. Unlike traditional methods, it uses a fixed computational grid and follows the heat carriers backward in time. The method 1) is accurate, 2) is unconditionally stable, 3) can deal with complex geometries without a large increase in computational cost, and 4) can be used for solving coupled equations using other numerical schemes. First, the numerical scheme is described. Then, simulations for transient and steady-state phonon transport in dielectric thin films are discussed. Numerical results are compared with analytical and reported numerical solutions and good agreement is obtained.

Issue Section:
Micro/Nanoscale Heat Transfer
Keywords:
heat conduction, phonons, dielectric thin films, Heat Conduction, Microscale, Nanoscale, Heat Transfer, Boltzmann Transport Equation
Topics:
Heat conduction, Microscale devices, Phonons, Steady state, Thin films, Transients (Dynamics), Temperature, Heat, Boundary-value problems, Electromagnetic scattering, Radiation scattering, Scattering (Physics)
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