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.
Modified Method of Characteristics for Simulating Microscale Energy Transport
Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division June 11, 2003; revision received February 20, 2004. Associate Editor: C. P. Grigoropoulos.
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Pilon, L., and Katika, K. M. (November 16, 2004). "Modified Method of Characteristics for Simulating Microscale Energy Transport ." ASME. J. Heat Transfer. October 2004; 126(5): 735–743. https://doi.org/10.1115/1.1795233
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