Direct simulation Monte Carlo

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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/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).

DSMC Software[edit]

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.[7]
  • dsmcFoam+ is the updated release of dsmcFoam. For further information, please go to the reference article.[8]
  • MONACO is a DSMC solver devised at Cornell University by Dr. Stefan Dietrich and Prof. Iain Boyd's Nonequilibrium Gas and Plasma Dynamics Laboratory at the University of Michigan.[9]
  • 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 principal 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.
  • DAC is a general purpose DSMC code developed by NASA at the Johnson Space and Langley Research Centers. It employs a two level mesh using Cartesian volumes and employs the cut cell algorithm developed by Prof. Tom Schwartzentruber's group at the University of Minnesota. Both scalar and parallel versions exist with the parallel version using the Message Passing Interface (MPI) and domain decomposition. DAC was designed to handle difficult problems such as complex geometries (for example, the International Space Station) and the plume impingement which may occur during the rendezvous of two spacecraft. DAC is classified as ITAR and distribution is restricted to United States users. Requests for DAC should be directed to the Technology Transfer Office at the NASA Johnson Space Center.
  • MAP (Multiphysics Algorithm with Particles) is another general purpose DSMC code developed by NASA at the Langley Research Center. It is an Octree-based 0D/2D/Axi/3D implementation of DSMC derived from DAC with emphasis placed on the high energy physics encountered upon re-entry flows. The cut cell algorithm used in MAP is derived from the algorithm used in SPARTA, which is based on the work done by Prof. Schwartzentruber's group at the University of Minnesota. MAP is classified as EAR99 and is freely available to US citizens and foreign entities upon request at
  • 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.
  • HAP (Hypersonic Aerothermodynamics Particle code) is a DSMC code developed at the U.S. Air Force Research Laboratory for high speed flight and space applications.
  • SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer), an Open Source 2 & 3D DSMC simulator optimized for parallel computing and developed at Sandia National Laboratories. Written in C++, SPARTA is designed to be easy to modify or extend with new functionality. Code is distributed under GPL, and available from the project website
  • PICLas is a parallel, three-dimensional PIC-DSMC solver developed cooperatively by the Institute of Space Systems and Institute of Aerodynamics and Gas Dynamics at the University of Stuttgart.[10] It is a flexible simulation suite for the computation of reactive plasma flows, where the PIC, DSMC and several other particle methods can be coupled or utilized separately. Application areas include the simulation of electric propulsion systems, atmospheric entry manoeuvres, gyrotons, travelling wave tubes and laser-plasma interaction. The free and open-source code is available under the GNU General Public License v3.0 at GitHub.
  • ultraSPARTS (ultra-fast Statistical PARTicle Simulation Package), owned by Plasma Taiwan Innovative Corp., is a commercial general-purpose DSMC package. It is written in C++ with important features including 2D/2D-axisymmetric/3D hybrid unstructured grid with parallel computing (MPI) using dynamic domain decomposition. A truly free of particle cloning technique is developed for handling 2D-axisymmetric flow. It has been applied to model many important science and engineering problems such as hypersonic non-reacting and reacting flow, turbo-vacuum pump flow, materials processing chamber design, large vacuum chamber design, materials processing (e.g., OLED, CIG deposition, PVD), RCS plume impingement of a spacecraft, and recently comet gas/dust plumes, among others. It also has been successfully hybridized with an unstructured-grid NS solver. Details can be found at Plasma Taiwan Innovative Corp.
  • VizGrain is a commercial, parallel, 1D/2D/3D, multi-species PIC-DSMC code developed by Esgee Technologies. VizGrain is designed to run standalone or coupled with fluid simulation for hybrid plasma modeling. Applications include semiconductor processing, reactive flows, electric propulsion, and material processing.
  • NFS (Nonequilibrium Flow Solver) is a 3D, multi-species, parallel DSMC code[11] with adaptive mesh refinement, developed at Non-equilibrium Flow Simulation Lab (NFSL) headed by Prof. Rakesh Kumar at Indian Institute of Technology Kanpur.


  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.
  7. ^ Scanlon, T.J; Roohi, E; White, C; Darbandi, M; Reese, J.M (2010). "An open source, parallel DSMC code for rarefied gas flows in arbitrary geometries" (PDF). Computers & Fluids. 39 (10): 2078–89. doi:10.1016/j.compfluid.2010.07.014.
  8. ^ White, C.; Borg, M.K.; Scanlon, T.J.; Longshaw, S.M.; John, B; Emerson, D.R.; Reese, J.M. (2010). "dsmcFoam+: An OpenFOAM based direct simulation Monte Carlo solver". Computer Physics Communications. 224: 22–43. doi:10.1016/j.cpc.2017.09.030.
  9. ^ Dietrich, Stefan; Boyd, Iain D (1996). "Scalar and Parallel Optimized Implementation of the Direct Simulation Monte Carlo Method". Journal of Computational Physics. 126 (2): 328–42. doi:10.1006/jcph.1996.0141.
  10. ^ Munz, Claus-Dieter; Auweter-Kurtz, Monika; Fasoulas, Stefanos; Mirza, Asim; Ortwein, Philip; Pfeiffer, Marcel; Stindl, Torsten (2014). "Coupled Particle-In-Cell and Direct Simulation Monte Carlo method for simulating reactive plasma flows". Comptes Rendus Mécanique. 342 (10–11): 662–70. doi:10.1016/j.crme.2014.07.005.
  11. ^ Kumar, Rakesh; Chinnappan, Arun Kumar (2017-12-15). "Development of a multi-species, parallel, 3D Direct Simulation Monte-Carlo solver for rarefied gas flows". Computers & Fluids. 159: 204–216. doi:10.1016/j.compfluid.2017.10.006. ISSN 0045-7930.

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