# 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 Tsein's parameter, which is equivalent to the product of Knudsen number and Mach number (KnM) or M$^2$/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 collision 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.

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).

## DSMC Software

Multiple implementations of the DSMC method exist:

• DS1V, DS2V and DS3V are the original DSMC programs written by Prof. Bird. These programs have a visual user interface that can be used for configuration and post processing.
• dsmcFoam is a DSMC solver for 2D and 3D flows. dsmcFoam is part of the open source CFD package OpenFOAM.
• MONACO is a DSMC solver developed by Prof. Iain Boyd's group at the University of Michigan.
• PI-DSMC is a commercial DSMC software package for 2D and 3D flows.
• SMILE (Statistical Modeling in Low-density Environment) is a general purpose 2D/3D parallel DSMC software system developed since 1998 by Computational Aerodynamics Laboratory (L7) at the Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Division of the Russian Academy of Sciences. SMILE has been the principle aerodynamic analysis tool for high-altitude stages of reentry of the Mir Space Station as well as many other Russian and European space vehicle projects.
• MGDS is a fully 3D DSMC solver incorporating three level adaptive mesh refinement and a cut cell algorithm developed by Prof. Tom Schwartzentruber's group at the University of Minnesota.
• Molflow is a 3D DSMC simulator currently developed at CERN for the simulation of free molecular flow (vacuum) systems.
• SAMADII/SCiV (Statistical Contact in Vacuum) is general purpose 3D DSMC software system based on multi-GPUs.

## References

1. ^ G. A. Bird, 'Approach to translational equilbrium in a rigid sphere gas', Phys. Fluids, 6, p1518 (1963).
2. ^ G. A. Bird, Molecular Gas Dynamics, Clarendon, Oxford (1976)
3. ^ G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Claredon, Oxford (1994)
4. ^ H. S. Tsein, 1948 ‘Superaerodynamics, mechanics of rarefied gases’ J. Aerospace Sci, 13, p342, 1946.
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).