CEAS Space Journal

, Volume 9, Issue 1, pp 127–137 | Cite as

Verification and validation of a parallel 3D direct simulation Monte Carlo solver for atmospheric entry applications

  • Paul Nizenkov
  • Peter Noeding
  • Martin Konopka
  • Stefanos Fasoulas
Original Paper


The in-house direct simulation Monte Carlo solver PICLas, which enables parallel, three-dimensional simulations of rarefied gas flows, is verified and validated. Theoretical aspects of the method and the employed schemes are briefly discussed. Considered cases include simple reservoir simulations and complex re-entry geometries, which were selected from literature and simulated with PICLas. First, the chemistry module is verified using simple numerical and analytical solutions. Second, simulation results of the rarefied gas flow around a \(70^{\circ }\) blunted-cone, the REX Free-Flyer as well as multiple points of the re-entry trajectory of the Orion capsule are presented in terms of drag and heat flux. A comparison to experimental measurements as well as other numerical results shows an excellent agreement across the different simulation cases. An outlook on future code development and applications is given.


Rarefied gas dynamics Atmospheric entry Direct simulation Monte Carlo Verification Validation 



P. Nizenkov wishes to thank the Landesgraduiertenförderung Baden-Württemberg and Airbus DS GmbH for supporting the research. Computational resources have been provided by the High Performance Computing Center Stuttgart (HLRS) of the University of Stuttgart.


  1. 1.
    Abe, T.: Inelastic collision model for vibrational-translational and vibrational-vibrational energy transfer in the direct simulation Monte Carlo method. Phys. Fluids. 6(9), 3175 (1994). doi: 10.1063/1.868094. http://link.aip.org/link/PHFLE6/v6/i9/p3175/s1&Agg=doi
  2. 2.
    Allègre, J., Bisch, D., Lengrand, J.C.: Experimental rarefied heat transfer at hypersonic conditions over 70-degree blunted cone. J. Spacecr. Rockets. 34(6), 724–728 (1997). doi: 10.2514/2.3302. http://arc.aiaa.org/doi/abs/10.2514/2.3302
  3. 3.
    Anderson, J.J.D.: Hypersonic and High-Temperature Gas Dynamics, 2nd edn. American Institute of Aeronautics and Astronautics, Reston ,VA (2006). doi: 10.2514/4.861956. http://arc.aiaa.org/doi/book/10.2514/4.861956
  4. 4.
  5. 5.
    Baganoff, D., McDonald, J.D.: A collision-selection rule for a particle simulation method suited to vector computers. Phys. Fluids A Fluid Dyn. 2(7), 1248–1259 (1990). doi: 10.1063/1.857625 CrossRefGoogle Scholar
  6. 6.
    Bird, G.A.: Molecular Gas Dynamics and the Direct Simulation of Gas Flows, 2nd edn. Oxford University Press, New York (1994)Google Scholar
  7. 7.
    Bird, G.A.: The DSMC Method. CreateSpace Independent Publishing Platform (2013)Google Scholar
  8. 8.
    Bird, G.A., Gallis, M.a., Torczynski, J.R., Rader, D.J.: Accuracy and efficiency of the sophisticated direct simulation Monte Carlo algorithm for simulating noncontinuum gas flows. Phys. Fluids. 21(1) (2009). doi: 10.1063/1.3067865
  9. 9.
    Borgnakke, C., Larsen, P.S.: Statistical collision model for Monte Carlo simulation of polyatomic gas mixture. J. Comput. Phys. 18(4), 405–420 (1975). doi: 10.1016/0021-9991(75)90094-7. http://linkinghub.elsevier.com/retrieve/pii/0021999175900947
  10. 10.
    Boyd, I.D.: Analysis of rotational nonequilibrium in standing shock waves of nitrogen. AIAA J. 28(11), 1997–1999 (1990). doi: 10.2514/3.10511. http://arc.aiaa.org/doi/abs/10.2514/3.10511
  11. 11.
    Boyd, I.D.: Analysis of vibrational-translational energy transfer using the direct simulation Monte Carlo method. Phys. Fluids A Fluid Dyn. 3(7), 1785 (1991). doi: 10.1063/1.857959. http://link.aip.org/link/PFADEB/v3/i7/p1785/s1&Agg=doi
  12. 12.
    Boyd, I.D.: Modeling backward chemical rate processes in the direct simulation Monte Carlo method. Phys. Fluids. 19(12), 126,103 (2007). doi: 10.1063/1.2825038. http://scitation.aip.org/content/aip/journal/pof2/19/12/10.1063/1.2825038
  13. 13.
    Boyd, I.D.: Computation of hypersonic flows using the direct simulation Monte Carlo method. J. Spacecr. Rockets 52(1), 38–53 (2015)CrossRefGoogle Scholar
  14. 14.
    Burt, J.M., Boyd, I.D.: A hybrid particle approach for continuum and rarefied flow simulation. J. Comput. Phys. 228(2), 460–475 (2009). doi: 10.1016/j.jcp.2008.09.022 CrossRefMATHGoogle Scholar
  15. 15.
    Gallis, M.A., Torczynski, J.R., Rader, D.J., Bird, G.A.: Convergence behavior of a new DSMC algorithm. J. Comput. Phys. 228(12), 4532–4548 (2009). doi: 10.1016/j.jcp.2009.03.021 CrossRefMATHGoogle Scholar
  16. 16.
    Gao, D., Zhang, C., Schwartzentruber, T.E.: Particle simulations of planetary probe flows employing automated mesh refinement. J. Spacecr. Rockets. 48(3), 397–405 (2011). doi: 10.2514/1.52129. http://arc.aiaa.org/doi/abs/10.2514/1.52129
  17. 17.
    Haas, B.L.: Fundamentals of chemistry modeling applicable to a vectorized particle simulation. In: 5th Joint Thermophysics and Heat Transfer Conference. AIAA, Reston, Virginia (1990). doi: 10.2514/6.1990-1749. http://arc.aiaa.org/doi/abs/10.2514/6.1990-1749
  18. 18.
    Haas, B.L., McDonald, J.D.: Validation of chemistry models employed in a particle simulation method. J. Thermophys. Heat Transfer. 7(1), 42–48 (1993). doi: 10.2514/3.11567. http://arc.aiaa.org/doi/abs/10.2514/3.11567
  19. 19.
    Ivanov, M.S., Markelov, G.N., Gimelshein, S.F.: Statistical simulation of reactive rarefied flows—numerical approach and applications. In: 7th AIAA/ASME Joint Thermophysics and Heat Transfer Conference. American Institute of Aeronautics and Astronautics, Reston, Virginia (1998). doi: 10.2514/6.1998-2669. http://arc.aiaa.org/doi/abs/10.2514/6.1998-2669
  20. 20.
    Alexander, J.F., Garcia, L.A.: The direct simulation Monte Carlo method. Comput. Phys. 11(6), 588–593 (1997). doi: 10.1063/1.168619 CrossRefGoogle Scholar
  21. 21.
    Klinkrad, H., Koppenwallner, G., Johannsmeier, D., Ivanov, M.S., Kashkovsky, A.V.: Free-molecular and transitional aerodynamics of spacecraft. Adv. Space Res. 16(12), 33–36 (1995). doi: 10.1016/0273-1177(95)98775-J CrossRefGoogle Scholar
  22. 22.
    Lighthill, M.J.: Dynamics of a dissociating gas Part I Equilibrium flow. J. Fluid Mech. 2(01), 1–32 (1957). doi: 10.1017/S0022112057000713. http://www.journals.cambridge.org/abstract_S0022112057000713
  23. 23.
    Moss, J.N., Boyles, K., Greene, F.A.: Orion Aerodynamics for Hypersonic Free Molecular to Continuum Conditions. In: 14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference, pp. 6–9. AIAA, Reston, Virginia (2006). doi: 10.2514/6.2006-8081. http://arc.aiaa.org/doi/abs/10.2514/6.2006-8081
  24. 24.
    Moss, J.N., Dogra, V.K., Price, J.M., Hash, D.B.: Comparison of DSMC and experimental results for hypersonic external flows. In: 30th AIAA Thermophysics Conference. AIAA, Reston, Virginia (1995). doi: 10.2514/6.1995-2028. http://arc.aiaa.org/doi/abs/10.2514/6.1995-2028
  25. 25.
    Munz, C.D., Auweter-Kurtz, M., Fasoulas, S., Mirza, A., Ortwein, P., Pfeiffer, M., Stindl, T.: Coupled Particle-in-cell and direct simulation Monte Carlo method for simulating reactive plasma flows. Comptes Rendus Mécanique 342(10–11), 662–670 (2014). doi: 10.1016/j.crme.2014.07.005. http://linkinghub.elsevier.com/retrieve/pii/S1631072114001442
  26. 26.
    Nizenkov, P., Noeding, P., Konopka, M., Reimann, B., Fasoulas, S.: Numerical Investigation of the Aerodynamics of the REX-Free Flyer in the Rarefied Gas Regime. In: 30th International Symposium on Rarefied Gas Dynamics (to be published). Victoria, BC, Canada (2016)Google Scholar
  27. 27.
    Ortwein, P., Binder, T., Copplestone, S., Mirza, A., Nizenkov, P., Pfeiffer, M., Stindl, T., Fasoulas, S., Munz, C.D.: Parallel Performance of a Discontinuous Galerkin Spectral Element Method Based PIC-DSMC Solver. In: High Performance Computing in Science and Engineering ’14, pp. 671–681. Springer International Publishing (2015). doi: 10.1007/978-3-319-10810-0_44. http://link.springer.com/10.1007/978-3-319-10810-0_44
  28. 28.
    Palharini, R.C., White, C., Scanlon, T.J., Brown, R.E., Borg, M.K., Reese, J.M.: Benchmark numerical simulations of rarefied non-reacting gas flows using an open-source DSMC code. Comput. Fluids. 120(1), 140–157 (2015). doi: 10.1016/j.compfluid.2015.07.021. http://linkinghub.elsevier.com/retrieve/pii/S0045793015002558
  29. 29.
    Pfeiffer, M., Mirza, A., Fasoulas, S.: A grid-independent particle pairing strategy for DSMC. J. Comput. Phys. 246, 28–36 (2013). doi: 10.1016/j.jcp.2013.03.018. http://linkinghub.elsevier.com/retrieve/pii/S0021999113001964
  30. 30.
    Pfeiffer, M., Nizenkov, P., Mirza, A., Fasoulas, S.: Direct simulation Monte Carlo modeling of relaxation processes in polyatomic gases. Phys. Fluids 28(2), 027,103 (2016). doi: 10.1063/1.4940989. http://dx.doi.org/10.1063/1.4940989
  31. 31.
    Scanlon, T.J., Roohi, E., White, C., Darbandi, M., Reese, J.M.: An open source, parallel DSMC code for rarefied gas flows in arbitrary geometries. Comput. Fluids 39(10), 2078–2089 (2010). doi: 10.1016/j.compfluid.2010.07.014. http://linkinghub.elsevier.com/retrieve/pii/S0045793010001891
  32. 32.
    Schaaf, S.A., Talbot, L.: Mechanics of Rarefied Gases. In: Glass, I.I., Hall, J.G. (eds.) NAVORD Report 1488: Handbook of Supersonic Aerodynamics, vol. 5, Section 16. Johns Hopkins University Applied Physics Laboratory, Silver Spring, Maryland (1959)Google Scholar
  33. 33.
    Schwartzentruber, T.E., Boyd, I.D.: Progress and future prospects for particle-based simulation of hypersonic flow. Prog. Aerosp. Sci. 72, 66–79 (2015). doi: 10.1016/j.paerosci.2014.09.003. http://linkinghub.elsevier.com/retrieve/pii/S0376042114000827
  34. 34.
    Stalder, J.R., Zurick, V.J.: Theoretical aerodynamic characteristics of bodies in a free-molecule-flow field. Tech. rep., Ames Aeronautical Laboratory, Moffett Field, California (1951). http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA381950
  35. 35.
    Wagner, W.: A convergence proof for Bird’s direct simulation Monte Carlo method for the Boltzmann equation. J. Stat. Phys. 66(3-4), 1011–1044 (1992). doi: 10.1007/BF01055714. http://link.springer.com/10.1007/BF01055714
  36. 36.
    Wilmoth, R.G., Blanchard, R.C., Moss, J.N.: Rarefied transitional bridging of blunt body aerodynamics. In: Brun, R. (ed.) Proceedings of the 21st International Symposium on Rarefied Gas Dynamics. Cépadues-Ed, Marseille, France (1999)Google Scholar

Copyright information

© CEAS 2016

Authors and Affiliations

  1. 1.Institute of Space Systems (IRS)University of StuttgartStuttgartGermany
  2. 2.Thermal EngineeringAirbus DS GmbHBremenGermany

Personalised recommendations