Three-dimensional simulations of two-phase liquid-vapor systems on GPU using the lattice Boltzmann method


  • A.L. Kupershtokh Lavrent′ev Institute of Hydrodynamics of SB RAS


lattice Boltzmann equation method, phase transitions, dynamics of multiphase flows, computer simulation, parallel computing, graphics processing units


The comparatively new lattice Boltzmann equation method (LBE) is a special discrete model of continuous media. Now, the LBE method is quite competitive with the traditional methods of computational fluid dynamics. The LBE method has considerable advantages, especially for multiphase and multicomponent flows. In the LBE method, the different phases of a substance are usually simulated as a one fluid. The algorithm of the LBE method is well suitable for parallelization on a large amount of stream processors that are available in modern Graphics Processing Units (GPU). The examples of 3D simulations of a spinodal decomposition, a breakdown of a thin liquid film due to the thermocapillary effect, and the process of breakdown of a 3D thin-wall liquid bubble are discussed. The speedup is about 70-90 times.

Author Biography

A.L. Kupershtokh


  1. McNamara G.R., Zanetti G. Use of the Boltzmann equation to simulate lattice-gas automata // Physical Review Letters. 1988. 61, N 20. 2332-2335.
  2. Higuera F.J., Jiménez J. Boltzmann approach to lattice gas simulations // Europhys. Lett. 1989. 9, N 7. 663-668.
  3. Chen S., Doolen G.D. Lattice Boltzmann method for fluid flow // Annu. Rev. Fluid Mech. 1998. 30. 329-364.
  4. Aidun C.K., Clausen J.R. Lattice-Boltzmann method for complex flows // Annu. Rev. Fluid Mech. 2010. 42. 439-472.
  5. Li W., Wei X., Kaufman A. Implementing lattice Boltzmann computation on graphics hardware // Visual Computer. 2003. 19. 444-456.
  6. Tölke J., Krafczyk M. TeraFLOP computing on a desktop PC with GPU for 3D CFD // Int. J. of Computational Fluid Dynamics. 2008. 22, N 7. 443-456.
  7. Janssen C., Krafczyk M. Free surface flow simulations on GPGPU using the LBM // Computers and Mathematics with Applications. 2011. 61, N 12. 3549-3563.
  8. Obrecht C., Kuznik F., Tourancheau B., Roux J.-J. Multi-GPU implementation of the lattice Boltzmann method // Computers and Mathematics with Applications. 2011.
    doi 10.1016/j.camwa.2011.02.020
  9. Грачев Н.Е., Дмитриев А.В., Сенин Д.С. Моделирование динамики газа при помощи решеточного метода Больцмана // Вычислительные методы и программирование. 2011. 12. 227-231.
  10. Broadwell J.E. Study of rarefied shear flow by the discrete velocity method // J. Fluid Mech. 1964. 19. 401-414.
  11. Qian Y.H., Orzag S.A. Lattice BGK models for the Navier-Stokes equation: Nonlinear deviation in compressible regimes // Europhys. Lett. 1993. 21. 255-259.
  12. Bhatnagar P.L., Gross E.P., Krook M.K. A model for collision process in gases. I. Small amplitude process in charged and neutral one-component system // Physical Review. 1954. 94, N 3. 511-525.
  13. Koelman J.M. V.A. A simple lattice Boltzmann scheme for Navier-Stokes fluid flow // Europhys. Lett. 1991. 15, N 6. 603-607.
  14. Kupershtokh A.L. Calculations of the action of electric forces in the lattice Boltzmann equation method using the difference of equilibrium distribution functions // Докл. VII Межд. научн. конф. «Современные проблемы электрофизики и электрогидродинамики жидкостей». Санкт-Петербург, 2003. 152-155.
  15. Kupershtokh A.L. New method of incorporating a body force term into the lattice Boltzmann equation // Proc. of the 5th Int. EHD Workshop. Poitiers (France), 2004. 241-246.
  16. Куперштох А.Л. Учет действия объемных сил в решеточных уравнениях Больцмана // Вестн. НГУ. Серия «Математика, механика и информатика». 2004. 4, № 2. 75-96.
  17. Kupershtokh A.L. Criterion of numerical instability of liquid state in LBE simulations // Computers and Mathematics with Applications. 2010. 59, N 7. 2236-2245.
  18. Ginzburg I., Adler P.M. Boundary flow condition analysis for the three-dimensional lattice Boltzmann model // J. Phys. II France. 1994. 4, N 2. 191-214.
  19. Shan X., Chen H. Lattice Boltzmann model for simulating flows with multiple phases and components // Physical Review E. 1993. 47, N 3. 1815-1819.
  20. Qian Y.H., Chen S. Finite size effect in lattice-BGK models // Int. J. of Modern Physics C. 1997. 8, N 4. 763-771.
  21. Zhang R., Chen H. Lattice Boltzmann method for simulations of liquid-vapor thermal flows // Phys. Rev. E. 2003. 67, N 6. 066711.
  22. Куперштох А.Л. Моделирование течений с границами раздела фаз жидкость-пар методом решеточных уравнений Больцмана // Вестн. НГУ. Серия «Математика, механика и информатика». 2005. 5, № 3. 29-42.
  23. Kupershtokh A.L., Karpov D.I., Medvedev D.A., Stamatelatos C.P., Charalambakos V.P., Pyrgioti E.C., Agoris D.P. Stochastic models of partial discharge activity in solid and liquid dielectrics // IET Science, Measurement and Technology. 2007. 1, N 6. 303-311.
  24. Kupershtokh A.L., Medvedev D.A., Karpov D.I. On equations of state in a lattice Boltzmann method // Computers and Mathematics with Applications. 2009. 58, N 5. 965-974.
  25. Kupershtokh A.L. A lattice Boltzmann equation method for real fluids with the equation of state known in tabular form only in regions of liquid and vapor phases // Computers and Mathematics with Applications. 2011. 61, N 12. 3537-3548.
  26. He X., Shan X., Doolen G.D. Discrete Boltzmann equation model for nonideal gases // Phys. Rev. E. 1998. 57, N 1. R13-R16.
  27. Guo Z., Zheng C., Shi B. Discrete lattice effects on the forcing term in the lattice Boltzmann method // Phys. Rev. E. 2002. 65, N 4. 046308(6).
  28. NVIDIA CUDA C. Programming Guide. Version 4.0. 2011.



How to Cite

Куперштох А.Л. Three-Dimensional Simulations of Two-Phase Liquid-Vapor Systems on GPU Using the Lattice Boltzmann Method // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2012. 13. 130-138



Section 1. Numerical methods and applications