Variance-reduced particle simulation of the Boltzmann transport equation in the relaxation-time approximation
Author(s)Radtke, Gregg A.; Hadjiconstantinou, Nicolas
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We present an efficient variance-reduced particle simulation technique for solving the linearized Boltzmann transport equation in the relaxation-time approximation used for phonon, electron, and radiative transport, as well as for kinetic gas flows. The variance reduction is achieved by simulating only the deviation from equilibrium. We show that in the limit of small deviation from equilibrium of interest here, the proposed formulation achieves low relative statistical uncertainty that is also independent of the magnitude of the deviation from equilibrium, in stark contrast to standard particle simulation methods. Our results demonstrate that a space-dependent equilibrium distribution improves the variance reduction achieved, especially in the collision-dominated regime where local equilibrium conditions prevail. We also show that by exploiting the physics of relaxation to equilibrium inherent in the relaxation-time approximation, a very simple collision algorithm with a clear physical interpretation can be formulated.
DepartmentMassachusetts Institute of Technology. Department of Mechanical Engineering
Physical Review E
American Physical Society
Radtke, Gregg A., and Nicolas G. Hadjiconstantinou. “Variance-reduced particle simulation of the Boltzmann transport equation in the relaxation-time approximation.” Physical Review E 79.5 (2009): 056711.(C) 2010 The American Physical Society.
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