# Direct simulation Monte Carlo

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 Prof. Graeme Bird,[1][2][3] 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${\displaystyle ^{2}}$/Re, where Re is the Reynolds number.[4][5] 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 simulation molecules which represent a large number of real molecules in a probabilistic simulation 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. The fundamental assumption of the DSMC method is that the molecular movement and collision phases can be decoupled over time periods that are smaller than the mean collision time. Various collision models are presented in.[6]

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 micro-electro-mechanical systems (MEMS).

## References

1. ^ Bird, G. A (1963). "Approach to Translational Equilibrium in a Rigid Sphere Gas". Physics of Fluids. 6 (10): 1518. doi:10.1063/1.1710976.
2. ^ G. A. Bird, Molecular Gas Dynamics, Clarendon, Oxford (1976)[page needed]
3. ^ G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Claredon, Oxford (1994)[page needed]
4. ^ Tsien, Hsue-Shen (1946). "Superaerodynamics, Mechanics of Rarefied Gases". Journal of the Aeronautical Sciences. 13 (12): 653–64. doi:10.2514/8.11476.
5. ^ M. N. Macrossan, 'Scaling Parameters for Hypersonic Flow: Correlation of Sphere Drag Data'. In: M. S. Ivanov and A. K. Rebrov, 25th International Symposium on Rarefied Gas Dynamics, Siberian Division of the Russian Academy of Sciences, p.759 (2007).
6. ^ Roohi, E.; Stefanov, S. (2016). "Collision partner selection schemes in DSMC: From micro/nano flows to hypersonic flows". Physics Reports. 656 (1): 1–38. doi:10.1016/j.physrep.2016.08.002.