In 1963, Graeme Bird published a short article in * Physics of
Fluids* [1] in which he described a stochastic algorithm for
simulating gas dynamics at the molecular scale. This numerical
method, which today is known as Direct Simulation Monte Carlo [2],
had a tremendous impact on the development of theoretical and
applied kinetic theory where it became the dominant computational
technique.

From the time of its introduction, during the early years of space exploration, DSMC has been widely used by the aerospace community, from applied mathematicians to design engineers [3]. Increasingly one finds DSMC used in mechanical engineering to simulate nano-scale flows, where the mean free path is comparable to the characteristic length scale of the flow [4,5,6].

Since DSMC is a stochastic algorithm for solving the full, nonlinear Boltzmann equation [7] the method and its variants also has many applications in physics and chemistry, such as plasmas [8,9], gas-phase reactions [10,11], and planetary atmospheres [12]. One of the more recent applications is in the simulation of granular gases [13,14,15]. DSMC is also used extensively in the applied mathematics community, particularly in the field of stochastic processes [16,17] and for the simulation of a variety of kinetic equations (e.g., traffic flow [18]).

Many improvements and extensions to DSMC have been introduced, especially in the past few years. For example, there are several variants that generalize the method to the simulation of dense gases [19,20,21] and liquids [22]. A highly efficient DSMC variant proposed recently by Malevanets and Kapral [23] is a promising alternative for model the dynamics of dilute suspensions. By combining a particle scheme, such as DSMC, with a conventional hydrodynamic computation (e.g., numerically solving the Navier-Stokes equations) allows one to span from microscopic to macroscopic scales; the development of such hybrids is an active branch of study in computational fluid mechanics [24,25,26].

[1] G.A. Bird,

[2] G. A. Bird,

[3] M.S. Ivanov and S.F. Gimelshein,

[4] F. Alexander, A. Garcia and B. Alder,

[5] N.G. Hadjiconstantinou and O. Simek,

[6] Q. Sun and I.D. Boyd,

[7] Cercignani, C.,

[8] A. Vasenkov and B.D. Shizgal,

[9] K. Nanbu,

[10] F. Baras and M. Malek Mansour,

[11] A. Lemarchand and B. Nowakowski,

[12] J. Zhang, D. B. Goldstein, P.L. Varghese, N.E. Gimelshein, S.F. Gimelshein, D.A. Levin, and L. Trafton,

[13] H.J. Herrmann and S. Luding,

[14] D. Risso and P. Cordero,

[15] A. Frezzotti,

[16] W. Wagner.

[17] S. Rjasanow and W. Wagner,

[18] A. Klar, B. Aw, T. Materne, and M. Rascle,

[19] F. Alexander, A. Garcia and B. Alder,

[20] A. Frezzotti.

[21] J.M. Montanero and A. Santos,

[22] N. Hadjiconstantinou, A. Garcia, and B. Alder,

[23] A. Malevanets and R. Kapral,

[24] J. Eggers and A. Beylich,

[25] S. Tiwari and A. Klar,

[26] A. Garcia, J. Bell, Wm. Y. Crutchfield and B. Alder,

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