Direct simulation Monte Carlo (DSMC) method uses probabilistic Monte Carlo simulation to solve the Boltzmann equation for finite Knudsen number fluid flows. The DSMC method was proposed by Graeme Bird, emeritus professor of aeronautics, University of Sydney. DSMC is a numerical method for modeling rarefied gas flows, in which the mean free path of a molecule is of the same order (or greater) than a representative physical length scale (i.e. the Knudsen number Kn is greater than 1). In supersonic and hypersonic flows rarefaction is characterized by Tsien's parameter, which is equivalent to the product of Knudsen number and Mach number (KnM) or M/Re, where Re is the Reynolds number. In these rarefied flows, the Navier-Stokes equations can be inaccurate. The DSMC method has been extended to model continuum flows (Kn < 1) and the results can be compared with Navier Stokes solutions. The DSMC method models fluid flows using probabilistic simulation molecules to solve the Boltzmann equation. Molecules are moved through a simulation of physical space in a realistic manner that is directly coupled to physical time such that unsteady flow characteristics can be modeled. Intermolecular collisions and molecule-surface collisions are calculated using probabilistic, phenomenological models. Common molecular models include the hard sphere model, the variable hard sphere (VHS) model, and the variable soft sphere (VSS) model. Various collision models are presented in. Currently, the DSMC method has been applied to the solution of flows ranging from estimation of the Space Shuttle re-entry aerodynamics to the modeling of microelectromechanical systems (MEMS). DSMC Algorithm The direct simulation Monte Carlo algorithm is like molecular dynamics in that the state of the system is given by the positions and velocities of the particles, , for . Unlike molecular dynamics, each particle in a DSMC simulation represents molecules in the physical system that have roughly at the same position and velocity. This allows DSMC to rescale length and time for the modeling of macroscopic systems (e.g., atmospheric entry). Specifically, the system volume is , where is the number density and each collision between simulation particles represents collisions among molecules in the physical system. As a rule of thumb there should be 20 or more particles per cubic mean free path for accurate results. The evolution of the system is integrated in time steps, , which are typically on the order of the mean collision time for a particle. At each time step all