Low-noise Monte Carlo simulation of the variable hard sphere gas

Physics of Fluids

Volumn 23, Issue 3, 2011, Pages

  Radtke, Gregg A ^a   Hadjiconstantinou, Nicolas G ^a   Wagner, Wolfgang ^b  

^a Massachusetts Institute of Technology Cambridge   (United States)

^b WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOLTZMANN EQUATION; INTELLIGENT SYSTEMS;

BOLTZMANN TRANSPORT EQUATION; DIRECT SIMULATION MONTE CARLO METHOD; EFFICIENT SIMULATION; MONTE CARLO APPROACH; MULTIDIMENSIONAL PROBLEMS; PARTICLE SIMULATION METHOD; STATISTICAL UNCERTAINTY; TRANSITION REGIMES;

MONTE CARLO METHODS;

EID: 79953271239     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3558887     Document Type: Article

References (41)

1. Hadjiconstantinou NG, Simek O. Constant-wall-temperature Nusselt number in micro and nano-channels. J. Heat Transfer 2002, 124:356. JHTRAO, 0022-1481, 10.1115/1.1447931,
2. Hadjiconstantinou NG. Dissipation in small scale gaseous flows. J. Heat Transfer 2003, 125:944. JHTRAO, 0022-1481, 10.1115/1.1571088,
3. Alexeenko AA, Gimelshein SF, Muntz EP, Ketsdever AD. Kinetic modeling of temperature driven flows in short microchannels. Int. J. Therm. Sci. 2006, 45:1045. IJTSFZ, 1290-0729, 10.1016/j.ijthermalsci.2006.01.014,
4. Hadjiconstantinou NG. The limits of Navier-Stokes theory and kinetic extensions for describing small-scale gaseous hydrodynamics. Phys. Fluids 2006, 18:111301. PHFLE6, 1070-6631, 10.1063/1.2393436,
5. Han YL, Muntz EP, Alexeenko A, Markus Y. Experimental and computational studies of temperature gradient-driven molecular transport in gas flows through nano/microscale channels. Nanoscale Microscale Thermophys. Eng. 2007, 11:151. NMTECW, 1556-7265, 10.1080/15567260701337209,
6. Cercignani C. Slow Rarefied Flows: Theory and Application to Micro-Electro-Mechanical Systems 2006, (Birkhauser-Verlag, Basel, ).
7. Bird GA. Molecular Gas Dynamics and the Direct Simulation of Gas Flows 1994, (Clarendon, Oxford, ).
8. Hadjiconstantinou NG, Garcia AL, Bazant MZ, He G. Statistical error in particle simulations of hydrodynamic phenomena. J. Comput. Phys. 2003, 187:274. JCTPAH, 0021-9991, 10.1016/S0021-9991(03)00099-8,
9. Baker LL, Hadjiconstantinou NG. Variance reduction for Monte Carlo solutions of the Boltzmann equation. Phys. Fluids 2005, 17:051703. PHFLE6, 1070-6631, 10.1063/1.1899210,
10. Asmussen S, Glynn PW. Stochastic Simulation: Algorithms and Analysis 2007, and, (Springer, New York, ).
11. Baker LL, Hadjiconstantinou NG. Variance reduction in particle methods for solving the Boltzmann equation. Proceedings of the 4th International Conference on Nanochannels, Microchannels, and Minichannels 2006, 377-383. and,,, Limerick, Ireland (ASME, New York, )
12. Homolle TM M, Hadjiconstantinou NG. Low-variance deviational simulation Monte Carlo. Phys. Fluids 2007, 19:041701. PHFLE6, 1070-6631, 10.1063/1.2717721,
13. Homolle TM M, Hadjiconstantinou NG. A low-variance deviational simulation Monte Carlo for the Boltzmann equation. J. Comput. Phys. 2007, 226:2341. JCTPAH, 0021-9991, 10.1016/j.jcp.2007.07.006,
14. Baker LL, Hadjiconstantinou NG. Variance-reduced particle methods for solving the Boltzmann equation. J. Comput. Theor. Nanosci. 2008, 5:165. JCTNAB, 1546-1955,
15. Chun J, Koch DL. A direct simulation Monte Carlo method for rarefied gas flows in the limit of small Mach number. Phys. Fluids 2005, 17:107107. PHFLE6, 1070-6631, 10.1063/1.2107807,
16. Al-Mohssen HA, Hadjiconstantinou NG. Low-variance direct Monte Carlo using importance weights. Math. Modell. Numer. Anal. 2010, 44:1069. MMNAAB, 0764-583X, 10.1051/m2an/2010052,
17. Öttinger HC. Stochastic Processes in Polymeric Fluids 1995, (Springer-Verlag, New York, ).
18. Wagner NJ, Öttinger HC. Accurate simulation of linear viscoelastic properties by variance reduction through the use of control variates. J. Rheol. 1997, 41:757. JORHD2, 0148-6055, 10.1122/1.550831,
19. Cercignani C. Mathematical Methods in Kinetic Theory 1990, 2nd ed. (Plenum, New York, ).
20. Cercignani C. The Boltzmann Equation and Its Applications 1988, (Springer Verlag, New York, ).
21. Radtke GA, Hadjiconstantinou NG. Variance-reduced particle simulation of the Boltzmann transport equation in the relaxation-time approximation. Phys. Rev. E 2009, 79:056711. PLEEE8, 1063-651X, 10.1103/PhysRevE.79.056711,
22. Hadjiconstantinou NG, Radtke GA, Baker LL. On variance reduced simulations of the Boltzmann transport equation for small-scale heat transfer applications. J. Heat Transfer 2010, 132:112401. JHTRAO, 0022-1481, 10.1115/1.4002028,
23. Wagner W. Deviational particle Monte Carlo for the Boltzmann equation. Monte Carlo Meth. Appl. 2008, 14:191. MCMAC6, 0929-9629, 10.1515/MCMA.2008.010,
24. Bird GA. Monte Carlo simulation in an engineering context. Prog. Astronaut. Aeronaut. 1981, 74:239. PAAEA9, 0079-6050,
25. Cercignani C, Daneri A. Flow of a rarefied gas between two parallel plates. J. Appl. Phys. 1963, 34:3509. JAPIAU, 0021-8979, 10.1063/1.1729249,
26. Radtke GA, Hadjiconstantinou NG, Wagner W. Low variance particle simulations of the Boltzmann transport equation for the variable hard sphere collision model. Proceedings of the 27th International Symposium on Rarefied Gas Dynamics 2011, D. A. Levin, I. J. Wysong, A. L. Garcia, and,, in, Pacific Grove, CA, edited by,, and (AIP, Melville, NY, ).
27. Wakefield JC, Gelfand AE, Smith AF M. Efficient generation of random variates via the ratio-of-uniforms method. Stat. Comput. 1991, 1:129. STACE3, 0960-3174, 10.1007/BF01889987,
28. Loyalka SK, Cipolla JW. Thermal creep slip with arbitrary accommodation at the surface. Phys. Fluids 1971, 14:1656. PHFLE6, 1070-6631, 10.1063/1.1693661,
29. Loyalka SK, Petrellis N, Storvick TS. Some numerical results for the BGK model: Thermal creep and viscous slip problems with arbitrary accommodation at the surface. Phys. Fluids 1975, 18:1094. PHFLE6, 1070-6631, 10.1063/1.861293,
30. Allshouse MR, Hadjiconstantinou NG. Low-variance deviational Monte Carlo simulations of pressure driven flow in micro- and nanoscale channels. Proceedings of the 26th International Symposium on Rarefied Gas Dynamics 2008, 1015-1020. T. Abe, and,, in, Kyoto, Japan, edited by (AIP, Melville, NY, )
31. Knudsen M. Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren. Ann. Phys. 1909, 333:75. ANPYA2, 0003-3804, 10.1002/andp.19093330106,
32. Rader DJ, Gallis MA, Torczynski JR, Wagner W. DSMC convergence behavior of the hard-sphere-gas thermal conductivity for Fourier heat flow. Phys. Fluids 2006, 18:077102. PHFLE6, 1070-6631, 10.1063/1.2213640,
33. Ohwada T. Higher order approximation methods. J. Comput. Phys. 1998, 139:1. JCTPAH, 0021-9991, 10.1006/jcph.1997.5869,
34. Doi T. Numerical analysis of the Poiseuille flow and the thermal transpiration of a rarefied gas through a pipe with a rectangular cross section based on the linearized Boltzmann equation for a hard sphere molecular gas. J. Vac. Sci. Technol. A 2010, 28:603. JVTAD6, 0734-2101, 10.1116/1.3449056,
35. For thermal creep with Kn=0.1 and Ly/Lx=2, Doi (Ref. c34) reported a value of mT=0.048 compared to 0.0473 for the LVDSMC method. Due to the small number of digits in the reported value, it was not possible to determine if 1% agreement was attained for this specific case.
36. Manela A, Hadjiconstantinou NG. Gas-flow animation by unsteady heating in a microchannel. Phys. Fluids 2010, 22:062001. PHFLE6, 1070-6631, 10.1063/1.3437602,
37. Cheremisin FG. Solving the Boltzmann equation in the case of passing to the hydrodynamic flow regime. Dokl. Phys. 2000, 45:401. DOPHFU, 1028-3358, 10.1134/1.1310733,
38. Caflisch RE, Pareschi L. Transport in Transition Regimes 2004, 135:57-73. N. Ben Abdallah, A. Arnold, P. Degond, I. M. Gamba, R. T. Glassey, C. D. Levermore, C. Ringhofer, and, in, edited by and (Springer-Verlag, New York, )
39. Wagner W. Stochastic models in kinetic theory. Phys. Fluids 2011, 23:030602. PHFLE6, 1070-6631,
40. Cercignani C, Daneri A. Elementary solutions of the linearized gas-dynamics Boltzmann equation and their application to the slip-flow problem. Ann. Phys. 1962, 20:219. ANPYA2, 0003-3804, 10.1016/0003-4916(62)90199-9,
41. Albertoni S, Cercignani C, Gotusso L. Numerical evaluation of the slip coefficient. Phys. Fluids 1963, 6:993. PHFLE6, 1070-6631, 10.1063/1.1706857,