Unified gas-kinetic particle method for dilute granular flow and its application in a solid jet

  • Zhao Wang
  • Hong YanEmail author
Research Paper


Because of its complexity, the problem of multiscale structure in granular flow has been receiving increasing attention. In this work, in order to conduct an in-depth exploration of the multiscale structure, a unified gas-kinetic particle (UGKP) method suitable for granular flow is constructed, in which the collision damping term and return-to-isotropy term are added to characterize the collision between particles. For the above two collision terms, the former characterizes the inelastic collision of particles, while the latter emphasizes the importance of the isotropic distribution of particles, which makes the results more reliable and reasonable. The construction of unified gas-kinetic schemes (UGKS) for granular flow has been reported in previous research. However, because of the need for discrete velocity space, the calculation size is quite large, making it impossible to use UGKS directly to investigate the multiscale problem. However, for UGKP, the flux contributed by particle free transport is calculated by free-streaming particles instead of discrete velocity space so that the corresponding calculation is much smaller than UGKS. The validity of the method is verified by numerical simulation of the solid jet compared with the particle-in-cell (PIC) method. In addition, since the sampled particles are used to obtain the flux contributed by the free transport, UGKP is more efficient than UGKS for solving multiscale problems.


Granular flow UGKP Multiscale Return-to-isotropy 



This work was supported by the Science Challenge Project (Grant TZ2016001). The authors would like to thank Yajun Zhu and Dr. Chang Liu for their helpful discussions.


  1. 1.
    Tenneti, S., Garg, R., Hrenya, C., et al.: Direct numerical simulation of gas-solid suspensions at moderate reynolds number: quantifying the coupling between hydrodynamic forces and particle velocity fluctuations. Powder Technol. 203(1), 57–69 (2010)CrossRefGoogle Scholar
  2. 2.
    Baer, M.R., Nunziato, J.W.: A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials. Int. J. Multiphase Flow 12(6), 861–889 (1986)CrossRefGoogle Scholar
  3. 3.
    O’Rourke, P.J., Snider, D.M.: Inclusion of collisional return-to-isotropy in the MP-PIC method. Chem. Eng. Sci. 80, 39–54 (2012)CrossRefGoogle Scholar
  4. 4.
    Bird, G.A., Brady, J.M.: Molecular gas dynamics and the direct simulation of gas flows. Clarendon press, Oxford (1994)Google Scholar
  5. 5.
    Fox, R.O.: A quadrature-based third-order moment method for dilute gas-particle flows. J. Comput. Phys. 227(12), 6313–6350 (2008)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Wang, D., Zhou, Y.: Particle dynamics in dense shear granular flow. Acta Mech. Sinica 26(1), 91–100 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Gidaspow, D.: Multiphase flow and fluidization: continuum and kinetic theory descriptions. Academic press, New York (1994)zbMATHGoogle Scholar
  8. 8.
    Jackson, R.: The dynamics of fluidized particles. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  9. 9.
    Syamlal, M., Pannala, S.: Multiphase continuum formulation for gas-solids reacting flows. Comput Gas-Solids Flows React Syst Theory pp. 1–65 (2011)Google Scholar
  10. 10.
    Chen, X., Wang, J.: Mesoscale-structure-based dynamic multiscale method for gas-solid flow. Chem. Eng. Sci. 192, 864–881 (2018)CrossRefGoogle Scholar
  11. 11.
    Xu, K., Huang, J.: A unified gas-kinetic scheme for continuum and rarefied flows. J. Comput. Phys. 229(20), 7747–7764 (2010)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Huang, J., Xu, K., Yu, P.: A unified gas-kinetic scheme for continuum and rarefied flows II: multi-dimensional cases. Commun. Comput. Phys. 12(3), 662–690 (2012)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Huang, J., Xu, K., Yu, P.: A unified gas-kinetic scheme for continuum and rarefied flows. III: Microflow simulations. Commun. Comput. Phys. 14(5), 1147–1173 (2013)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Liu, C., Xu, K., Sun, Q., et al.: A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations. J. Comput. Phys. 314(5), 305–340 (2016)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Liu, C., Zhou, G., Shyy, W., et al.: Limitation principle for computational fluid dynamics. Shock Waves pp. 1–20 (2019)Google Scholar
  16. 16.
    Wang, Z., Yan, H., Li, Q., et al.: Unified gas-kinetic scheme for diatomic molecular flow with translational, rotational, and vibrational modes. J. Comput. Phys. 350, 237–259 (2017)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Xiao, T., Cai, Q., Xu, K.: A well-balanced unified gas-kinetic scheme for multiscale flow transport under gravitational field. J. Comput. Phys. 332, 475–491 (2017)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Xiao, T., Xu, K., Cai, Q., et al.: An investigation of non-equilibrium heat transport in a gas system under external force field. Int. J. Heat Mass Transf. 126, 362–379 (2018)CrossRefGoogle Scholar
  19. 19.
    Liu, C., Xu, K.: A unified gas kinetic scheme for continuum and rarefied flows. V: Multiscale and multi-component plasma transport. Commun. Comput. Phys. 22(5), 1175–1223 (2017)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Liu, C., Wang, Z., Xu, K.: A unified gas-kinetic scheme for continuum and rarefied flows VI: Dilute disperse gas-particle multiphase system. J. Comput. Phys. 386, 264–295 (2019)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Zhu, Y., Liu, C., Zhong, C., et al.: Unified gas-kinetic wave-particle methods. II: Multiscale simulation on unstructured mesh. Phys Fluids 31(6), 067105 (2019)CrossRefGoogle Scholar
  22. 22.
    O’Rourke, P.J., Snider, D.M.: An improved collision damping time for mp-pic calculations of dense particle flows with applications to polydisperse sedimenting beds and colliding particle jets. Chem. Eng. Sci. 65(22), 6014–6028 (2010)CrossRefGoogle Scholar
  23. 23.
    Xu, K.: Direct modeling for computational fluid dynamics: construction and application of unified gas-kinetic schemes. World Scientific, Singapore (2015)CrossRefGoogle Scholar
  24. 24.
    Press, W.H., Teukolsky, S.A., Vetterling, W.T., et al.: Numerical recipes 3rd edition: The art of scientific computing. Cambridge University Press, Cambridge (2007)zbMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Yangtze River Delta Research Institute of NPUNorthwestern Polytechnical UniversityTaicangChina
  2. 2.Shaanxi Key Laboratory of Internal Aerodynamics in Aero-EngineXi’anChina

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