Variance-reduced particle simulation of the Boltzmann transport equation in the relaxation-time approximation
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 o...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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American Physical Society
2010
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| Online Access: | http://hdl.handle.net/1721.1/51324 https://orcid.org/0000-0002-1670-2264 |
| _version_ | 1826198710141321216 |
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| author | Radtke, Gregg A. Hadjiconstantinou, Nicolas |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Radtke, Gregg A. Hadjiconstantinou, Nicolas |
| author_sort | Radtke, Gregg A. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:08:36Z |
| format | Article |
| id | mit-1721.1/51324 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:08:36Z |
| publishDate | 2010 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/513242022-10-01T01:34:37Z Variance-reduced particle simulation of the Boltzmann transport equation in the relaxation-time approximation Radtke, Gregg A. Hadjiconstantinou, Nicolas Massachusetts Institute of Technology. Department of Mechanical Engineering Hadjiconstantinou, Nicolas Radtke, Gregg A. Hadjiconstantinou, Nicolas 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. Singapore-MIT Alliance 2010-02-02T17:54:39Z 2010-02-02T17:54:39Z 2009-05 2009-04 Article http://purl.org/eprint/type/JournalArticle 1550-2376 1539-3755 http://hdl.handle.net/1721.1/51324 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. https://orcid.org/0000-0002-1670-2264 en_US http://dx.doi.org/10.1103/PhysRevE.79.056711 Physical Review E Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Radtke, Gregg A. Hadjiconstantinou, Nicolas Variance-reduced particle simulation of the Boltzmann transport equation in the relaxation-time approximation |
| title | Variance-reduced particle simulation of the Boltzmann transport equation in the relaxation-time approximation |
| title_full | Variance-reduced particle simulation of the Boltzmann transport equation in the relaxation-time approximation |
| title_fullStr | Variance-reduced particle simulation of the Boltzmann transport equation in the relaxation-time approximation |
| title_full_unstemmed | Variance-reduced particle simulation of the Boltzmann transport equation in the relaxation-time approximation |
| title_short | Variance-reduced particle simulation of the Boltzmann transport equation in the relaxation-time approximation |
| title_sort | variance reduced particle simulation of the boltzmann transport equation in the relaxation time approximation |
| url | http://hdl.handle.net/1721.1/51324 https://orcid.org/0000-0002-1670-2264 |
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