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MONTE CARLO METHODS FOR SOLVING THE BOLTZMANN TRANSPORT EQUATION

DOI: 10.1615/AnnualRevHeatTransfer.2014007381
pages 205-265

Jean-Philippe M. Peraud
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Colin D. Landon
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Nicolas G. Hadjiconstantinou
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA


MOTS CLÉS: Boltzmann equation, Monte Carlo, variance reduction, phonons, multiscale

Résumé

We review Monte Carlo methods for solving the Boltzmann equation for applications to small-scale transport processes, with particular emphasis on nanoscale heat transport as mediated by phonons. Our discussion reviews the numerical foundations of Monte Carlo algorithms, basic simulation methodology, as well as recent developments in the field. Examples of the latter include formulations for calculating the effective thermal conductivity of periodically nanostructured materials and variance-reduction methodologies for reducing the computational cost associated with statistical sampling of field properties of interest, such as the temperature and heat flux. Recent developments are presented in the context of applications of current practical interest, including multiscale problems that have motivated some of the most recent developments.

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