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1

Danforth, Amanda L., and Lyle N. Long. "Nonlinear acoustic simulations using direct simulation Monte Carlo." Journal of the Acoustical Society of America 116, no. 4 (October 2004): 1948–55. http://dx.doi.org/10.1121/1.1785614.

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2

Alexander, Francis J., and Alejandro L. Garcia. "The Direct Simulation Monte Carlo Method." Computers in Physics 11, no. 6 (1997): 588. http://dx.doi.org/10.1063/1.168619.

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3

Carlson, Ann B., and H. A. Hassan. "Radiation modeling with direct simulation Monte Carlo." Journal of Thermophysics and Heat Transfer 6, no. 4 (October 1992): 631–36. http://dx.doi.org/10.2514/3.11544.

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4

TSUTSUI, Shingo, and Keiichi FUTAGI. "The Application Example of Direct Simulation Monte Carlo Method to Turbo-molecular Pump." Journal of the Vacuum Society of Japan 58, no. 7 (2015): 253–56. http://dx.doi.org/10.3131/jvsj2.58.253.

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5

Alamatsaz, Arghavan, and Ayyaswamy Venkattraman. "Characterizing deviation from equilibrium in direct simulation Monte Carlo simulations." Physics of Fluids 31, no. 4 (April 2019): 042005. http://dx.doi.org/10.1063/1.5093732.

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6

Liou, William W., and Yichuan Fang. "Forced Couette flow simulations using direct simulation Monte Carlo method." Physics of Fluids 16, no. 12 (December 2004): 4211–20. http://dx.doi.org/10.1063/1.1801092.

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7

Lo, Ming-Chung, Chien-Yu Pan, and Jong-Shinn Wu. "On an Axisymmetric Direct Simulation Monte Carlo Method." International Journal of Computational Fluid Dynamics 35, no. 5 (May 28, 2021): 373–87. http://dx.doi.org/10.1080/10618562.2021.1955867.

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8

Hong, Andrew, and Aaron Morris. "Novel direct simulation Monte Carlo method for spherocylinders." Powder Technology 399 (February 2022): 117085. http://dx.doi.org/10.1016/j.powtec.2021.117085.

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9

Sharipov, Felix. "Direct Simulation Monte Carlo Method Applied to Aerothermodynamics." Journal of the Brazilian Society of Mechanical Sciences 23, no. 4 (2001): 441–52. http://dx.doi.org/10.1590/s0100-73862001000400005.

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10

Carlson, Ann B., and Richard G. Wilmoth. "Shock interference prediction using direct simulation Monte Carlo." Journal of Spacecraft and Rockets 29, no. 6 (November 1992): 780–85. http://dx.doi.org/10.2514/3.25531.

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11

CHAO, LIU, SANG KYU KWAK, and SANTOSH ANSUMALI. "DIRECT SIMULATION MONTE CARLO FOR DENSE HARD SPHERES." International Journal of Modern Physics C 25, no. 01 (December 2, 2013): 1340023. http://dx.doi.org/10.1142/s0129183113400238.

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We propose a modified direct simulation Monte Carlo (DSMC) method, which extends the validity of DSMC from rarefied to dense system of hard spheres (HSs). To assess this adapted method, transport properties of hard-sphere (HS) systems have been predicted both at dense states as well as dilute, and we observed the excellent accuracy over existing DSMC-based algorithms including the Enskog theory. The present approach provides an intuitive and systematic way to accelerate molecular dynamics (MD) via mesoscale approach.
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12

Gladkov, Denis, José-Juan Tapia, Samuel Alberts, and Roshan M. D’Souza. "Graphics processing unit based direct simulation Monte Carlo." SIMULATION 88, no. 6 (September 26, 2011): 680–93. http://dx.doi.org/10.1177/0037549711418787.

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13

USAMI, Masaru, Hajime KYOGOKU, and Seizo KATO. "Some Trials for the Monte Carlo Direct Simulation." Journal of the Japan Society for Aeronautical and Space Sciences 39, no. 450 (1991): 359–66. http://dx.doi.org/10.2322/jjsass1969.39.359.

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14

Alexander, Francis J., Alejandro L. Garcia, and Berni J. Alder. "Direct simulation Monte Carlo for thin‐film bearings." Physics of Fluids 6, no. 12 (December 1994): 3854–60. http://dx.doi.org/10.1063/1.868377.

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15

Ota, Masahiro, Hiroyoshi Taniguchi, and Masanori Aritomi. "Parallel Processings for Direct Simulation Monte Carlo Method." Transactions of the Japan Society of Mechanical Engineers Series B 61, no. 582 (1995): 496–502. http://dx.doi.org/10.1299/kikaib.61.496.

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16

Brey, J. Javier, and M. J. Ruiz-Montero. "Direct Monte Carlo simulation of dilute granular flow." Computer Physics Communications 121-122 (September 1999): 278–83. http://dx.doi.org/10.1016/s0010-4655(99)00331-8.

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17

Karabulut, Hasan, and Huriye Arıman Karabulut. "Stochastic theory of direct simulation Monte Carlo method." Theoretical Chemistry Accounts 122, no. 5-6 (March 6, 2009): 227–43. http://dx.doi.org/10.1007/s00214-009-0533-0.

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18

Kumar, D., and S. J. Thomson. "Implementing direct Monte Carlo simulation in batch mode." Computers and Electronics in Agriculture 12, no. 2 (March 1995): 163–71. http://dx.doi.org/10.1016/0168-1699(94)00042-o.

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19

Reggiani, Lino, Luca Varani, and Vladimir Mitin. "Direct Monte Carlo simulation of hot-carrier conductivity." Solid-State Electronics 32, no. 12 (December 1989): 1383–86. http://dx.doi.org/10.1016/0038-1101(89)90244-x.

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20

Oran, E. S., C. K. Oh, and B. Z. Cybyk. "DIRECT SIMULATION MONTE CARLO: Recent Advances and Applications." Annual Review of Fluid Mechanics 30, no. 1 (January 1998): 403–41. http://dx.doi.org/10.1146/annurev.fluid.30.1.403.

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21

Peter, William. "Quiet direct simulation Monte-Carlo with random timesteps." Journal of Computational Physics 221, no. 1 (January 2007): 1–8. http://dx.doi.org/10.1016/j.jcp.2006.06.008.

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22

Ikegawa, Masato, and Junichi Kobayashi. "Deposition Profile Simulation Using the Direct Simulation Monte Carlo Method." Journal of The Electrochemical Society 136, no. 10 (October 1, 1989): 2982–86. http://dx.doi.org/10.1149/1.2096387.

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23

Ikegawa, Masato, and Jun'ichi Kobayashi. "Semiconductor Deposition Profile Simulation Using Direct Simulation Monte Carlo Method." Transactions of the Japan Society of Mechanical Engineers Series B 59, no. 567 (1993): 3365–72. http://dx.doi.org/10.1299/kikaib.59.3365.

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24

Bruno, Domenico. "Direct simulation Monte Carlo simulation of thermal fluctuations in gases." Physics of Fluids 31, no. 4 (April 2019): 047105. http://dx.doi.org/10.1063/1.5093369.

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25

Giersz, Mirek. "Monte-Carlo Simulations." Symposium - International Astronomical Union 174 (1996): 101–10. http://dx.doi.org/10.1017/s0074180900001431.

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The revision of the Stodółkiewicz's Monte-Carlo code is presented. It treats each superstar as a single star and follows the evolution and motion of all individual stellar objects. The first calculations, for equalmass N-body systems with three-body energy generation accordingly to Spitzer's formulae, show good agreement with the direct N-body calculations for N = 2000 and 10000 particles.
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26

Moss, James N., and Graeme A. Bird. "Direct Simulation Monte Carlo Simulations of Hypersonic Flows With Shock Interactions." AIAA Journal 43, no. 12 (December 2005): 2565–73. http://dx.doi.org/10.2514/1.12532.

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27

Degond, Pierre, and Giacomo Dimarco. "Fluid simulations with localized boltzmann upscaling by direct simulation Monte-Carlo." Journal of Computational Physics 231, no. 6 (March 2012): 2414–37. http://dx.doi.org/10.1016/j.jcp.2011.11.030.

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28

Schullian, O., J. Loreau, N. Vaeck, A. van der Avoird, B. R. Heazlewood, C. J. Rennick, and T. P. Softley. "Simulating rotationally inelastic collisions using a direct simulation Monte Carlo method." Molecular Physics 113, no. 24 (October 27, 2015): 3972–78. http://dx.doi.org/10.1080/00268976.2015.1098740.

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29

Christou, Chariton, and S. Kokou Dadzie. "Direct-Simulation Monte Carlo Investigation of a Berea Porous Structure." SPE Journal 21, no. 03 (June 15, 2016): 0938–46. http://dx.doi.org/10.2118/173314-pa.

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Summary Shale-gas and tight gas reservoirs consist of porous structures with pore diameter in the range of 1 to 200 nm. At these scales, the pore diameter becomes comparable to the gas mean free path. Flows in these structures fail often in the transition and slip flow regimes. Standard continuum fluid methods such as the Navier-Stokes-Fourier (NSF) set of equations fail to describe flows of these regimes. We present a direct-simulation monte carlo (DSMC) study of a 3D porous structure in an unlimited parallel simulation. The 3D geometry was obtained with microcomputed-tomography (micro-CT). The gas considered is CH4 (100%), and the gas intermolecular-collision model for the simulation is the variable hard sphere (VHS). Simulations were carried out for three different Knudsen (Kn) numbers within the transition and slip flow regimes. The results demonstrate some of the significant differences that appear in gas-flow properties depending on the Kn number and the flow regime. In addition, the velocity profile appears to depend on the Kn number. At the inlet of the porous structures, more-uniform velocity profile occurs for the three Kn numbers. At the outlet, the velocity profile varies depending on the Kn number. For Kn ≈ 0.037, a parabolic shape is observed for the velocity profile, whereas a more-uniform shape is observed for Kn ≈ 3.7.
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30

Sengil, N., and U. Sengil. "2D hybrid meshes for direct simulation Monte Carlo solvers." Journal of Physics: Conference Series 410 (February 8, 2013): 012075. http://dx.doi.org/10.1088/1742-6596/410/1/012075.

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31

Danforth, Amanda L., and Lyle N. Long. "Acoustic propagation using the direct simulation Monte Carlo method." Journal of the Acoustical Society of America 114, no. 4 (October 2003): 2356–57. http://dx.doi.org/10.1121/1.4776795.

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32

Nanbu, K., S. Igarashi, and Y. Watanabe. "False collisions in the direct simulation Monte Carlo method." Physics of Fluids 31, no. 7 (1988): 2047. http://dx.doi.org/10.1063/1.866654.

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33

Molchanova, Alexandra N., Alexander V. Kashkovsky, and Yevgeniy A. Bondar. "Surface recombination in the direct simulation Monte Carlo method." Physics of Fluids 30, no. 10 (October 2018): 107105. http://dx.doi.org/10.1063/1.5048353.

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34

Frezzotti, A., P. Barbante, and L. Gibelli. "Direct simulation Monte Carlo applications to liquid-vapor flows." Physics of Fluids 31, no. 6 (June 2019): 062103. http://dx.doi.org/10.1063/1.5097738.

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35

Plimpton, S. J., S. G. Moore, A. Borner, A. K. Stagg, T. P. Koehler, J. R. Torczynski, and M. A. Gallis. "Direct simulation Monte Carlo on petaflop supercomputers and beyond." Physics of Fluids 31, no. 8 (August 2019): 086101. http://dx.doi.org/10.1063/1.5108534.

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36

Palaniswaamy, Geethpriya, and Sudarshan K. Loyalka. "Direct simulation Monte Carlo aerosol dynamics: Collisional sampling algorithms." Annals of Nuclear Energy 34, no. 1-2 (January 2007): 13–21. http://dx.doi.org/10.1016/j.anucene.2006.11.004.

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37

Palaniswaamy, Geethpriya, and Sudarshan K. Loyalka. "Direct simulation, Monte Carlo, aerosol dynamics: Coagulation and condensation." Annals of Nuclear Energy 35, no. 3 (March 2008): 485–94. http://dx.doi.org/10.1016/j.anucene.2007.06.024.

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38

Walenta, Z. A., and K. Lener. "Direct Monte-Carlo simulation of developing detonation in gas." Shock Waves 18, no. 1 (March 29, 2008): 71–75. http://dx.doi.org/10.1007/s00193-008-0131-4.

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39

Hadjiconstantinou, Nicolas G. "Analysis of discretization in the direct simulation Monte Carlo." Physics of Fluids 12, no. 10 (2000): 2634. http://dx.doi.org/10.1063/1.1289393.

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40

Myo, Kyaw Sett, Weidong Zhou, Kok Leong Lee, Shengkai Yu, and Wei Hua. "Direct Monte Carlo simulation of nanoscale mixed gas bearings." Advances in Mechanical Engineering 7, no. 6 (June 2, 2015): 168781401558952. http://dx.doi.org/10.1177/1687814015589528.

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41

Liffman, Kurt. "A direct simulation Monte-Carlo method for cluster coagulation." Journal of Computational Physics 100, no. 1 (May 1992): 116–27. http://dx.doi.org/10.1016/0021-9991(92)90314-o.

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42

UNGERER, PHILIPPE, ANNE BOUTIN, and ALAIN H. FUCHS. "Direct calculation of bubble points by Monte Carlo simulation." Molecular Physics 97, no. 4 (August 20, 1999): 523–39. http://dx.doi.org/10.1080/00268979909482852.

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43

UNGERER, ANNE BOUTIN, ALAIN H. FUCH, PHILIPPE. "Direct calculation of bubble points by Monte Carlo simulation." Molecular Physics 97, no. 4 (August 20, 1999): 523–39. http://dx.doi.org/10.1080/002689799163622.

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44

Garcia, Alejandro L., and Wolfgang Wagner. "Time step truncation error in direct simulation Monte Carlo." Physics of Fluids 12, no. 10 (2000): 2621. http://dx.doi.org/10.1063/1.1289691.

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45

White, C., M. K. Borg, T. J. Scanlon, S. M. Longshaw, B. John, D. R. Emerson, and J. M. Reese. "dsmcFoam+: An OpenFOAM based direct simulation Monte Carlo solver." Computer Physics Communications 224 (March 2018): 22–43. http://dx.doi.org/10.1016/j.cpc.2017.09.030.

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46

Mizuseki, H., Y. Jin, Y. Kawazoe, and L. T. Wille. "Cluster growth processes by direct simulation monte carlo method." Applied Physics A: Materials Science & Processing 73, no. 6 (December 1, 2001): 731–35. http://dx.doi.org/10.1007/s003390100911.

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47

Higdon, Kyle J., Brett A. Cruden, Aaron M. Brandis, Derek S. Liechty, David B. Goldstein, and Philip L. Varghese. "Direct Simulation Monte Carlo Shock Simulation of Saturn Entry Probe Conditions." Journal of Thermophysics and Heat Transfer 32, no. 3 (July 2018): 680–90. http://dx.doi.org/10.2514/1.t5275.

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48

Li, Yuan Ying, and De Sheng Zhang. "Plane Truss Reliability Numerical Simulation Based on MATLAB." Applied Mechanics and Materials 256-259 (December 2012): 1091–96. http://dx.doi.org/10.4028/www.scientific.net/amm.256-259.1091.

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Based on the basic principles of structure reliability numerical analysis, the numerical simulation of the displacement and stress reliability of plane truss under vertical load was programmed with MATLAB. The failure probability of the most unfavorable structural vertical displacement and stress and reliable indicators were obtained through direct sampling Monte Carlo method, response surface method, response surface-Monte Carlo method and response surface-important sampling Monte Carlo method. It is found that calculation lasts longer since there are so many samples with Monte-Carlo method, higher accuracy and less calculation time can be achieved through response surface-Monte Carlo method and response surface-important sampling Monte Carlo method with fewer samples. The results of different numerical simulation calculations are almost identical and reliable, providing references to reliability analysis of complex structures.
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49

Moss, James N. "Direct Simulation Monte Carlo Simulations of Ballute Aerothermodynamics Under Hypersonic Rarefied Conditions." Journal of Spacecraft and Rockets 44, no. 2 (March 2007): 289–98. http://dx.doi.org/10.2514/1.22706.

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50

Di Staso, G., H. J. H. Clercx, S. Succi, and F. Toschi. "Lattice Boltzmann accelerated direct simulation Monte Carlo for dilute gas flow simulations." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374, no. 2080 (November 13, 2016): 20160226. http://dx.doi.org/10.1098/rsta.2016.0226.

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Hybrid particle–continuum computational frameworks permit the simulation of gas flows by locally adjusting the resolution to the degree of non-equilibrium displayed by the flow in different regions of space and time. In this work, we present a new scheme that couples the direct simulation Monte Carlo (DSMC) with the lattice Boltzmann (LB) method in the limit of isothermal flows. The former handles strong non-equilibrium effects, as they typically occur in the vicinity of solid boundaries, whereas the latter is in charge of the bulk flow, where non-equilibrium can be dealt with perturbatively, i.e. according to Navier–Stokes hydrodynamics. The proposed concurrent multiscale method is applied to the dilute gas Couette flow, showing major computational gains when compared with the full DSMC scenarios. In addition, it is shown that the coupling with LB in the bulk flow can speed up the DSMC treatment of the Knudsen layer with respect to the full DSMC case. In other words, LB acts as a DSMC accelerator. This article is part of the themed issue ‘Multiscale modelling at the physics–chemistry–biology interface’.
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