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Computational Thermal Sciences: An International Journal
ESCI SJR: 0.249 SNIP: 0.434 CiteScore™: 1.4

ISSN Imprimir: 1940-2503
ISSN On-line: 1940-2554

Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.2011003187
pages 503-510

DSMC SCHEME TO STUDY THE NONLINEAR BOLTZMANN TRANSPORT EQUATION FOR PHONONS

Yusuke Masao
Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto, 606-8501, Japan
Mitsuhiro Matsumoto
Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto, 606-8501, Japan ; Advanced Research Institute of Fluid Science and Engineering, Graduate School of Engineering, Kyoto University, Kyoto, 606-8530,

RESUMO

A DSMC (direct simulation Monte Carlo) scheme is a method to solve a nonlinear Boltzmann transport equation (BTE) and widely used for analysis of rarefied gas dynamics. We adopt this scheme to study phonon dynamics in analogous with rarefied gas. Phonons are one of the dominant energy carriers in solid materials. Although heat conduction is generally described by the Fourier rule, this fails when spatial scale of the system becomes smaller. In this case, heat conduction should be described by the BTE which is often treated with the relaxation time approximation. However, our previous work with molecular dynamics (MD) simulation suggested that this has some limitations that couplings among phonons are not considered directly. We have developed a simulation code based on the DSMC scheme for analysis of phonon dynamics and carried out two test calculations. In the first case, we simulated the phonon dynamics in a large nonequilibrium situation. Relaxation behaviors similar to MD results were observed. In the second case, we simulated phonon dynamics at equilibrium to calculate the relaxation time, which is an input parameter in the relaxation time approximation. Thus the proposed DSMC scheme is a promising method for micro-scale heat conduction in solids.


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