Modeling of thermal flows in a medium with phase transitions using the lattice Boltzmann method


  • A.L. Kupershtokh Lavrent′ev Institute of Hydrodynamics of SB RAS
  • D.A. Medvedev Lavrent′ev Institute of Hydrodynamics of SB RAS
  • I.I. Gribanov Novosibirsk State University


lattice Boltzmann method, phase transitions, dynamics of multiphase fluids, heat and mass transfer, mesoscopic methods, computer simulations


A new method is proposed for the computation of heat and mass transfer for the modeling of flow of a medium with liquid-vapor phase transitions using the lattice Boltzmann equations (LBE). When the phase boundaries are present, it is necessary to consider the equation of energy transfer. A second set of LBE distribution functions is introduced in the form of a passive scalar that describes the transfer of internal energy. In order to eliminate the spurious diffusion of energy at the interface with a high density ratio, special pseudo-forces are introduced to prevent the passive scalar from expansion. The thermal conductivity and the pressure work are taken into account in the energy equation. The latent heat of evaporation and condensation is accounted in the energy equation for the inner region of a thin liquid-vapor transition layer. This allows one to avoid tracking the interfaces. Several simple tests were carried out to demonstrate all the aspects of the processes considered. It is shown that the Galilean invariance and the scaling of thermal conduction processes hold. The proposed method has a low scheme diffusion for the internal energy and can be applied for modeling a wide range of flows of two-phase media with the mass and heat transfer.

Author Biographies

A.L. Kupershtokh

D.A. Medvedev

I.I. Gribanov

Novosibirsk State University,
Department of Mathematics and Mechanics,
ул. Пирогова, 1, 630090, Новосибирск
• Student


  1. McNamara G.R., Zanetti G. Use of the Boltzmann equation to simulate lattice-gas automata // Phys. Rev. Lett. 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. Shan X., Chen H. Lattice Boltzmann model for simulating flows with multiple phases and components // Phys. Rev. E. 1993. 47, N 3. 1815-1819.
  6. Qian Y.-H., Chen S. Finite size effect in lattice-BGK models // Int. J. Mod. Phys. C. 1997. 8, N 4. 763-771.
  7. Куперштох А.Л. Трехмерное моделирование двухфазных систем типа жидкость-пар методом решеточных уравнений Больцмана на GPU // Вычислительные методы и программирование. 2012. 13. 130-138.
  8. Куперштох А.Л. Трехмерное моделирование методом LBE на гибридных GPU-кластерах распада бинарной смеси жидкого диэлектрика с растворенным газом на систему парогазовых каналов // Вычислительные методы и программирование. 2012. 13. 384-390.
  9. Бикулов Д.А., Сенин Д.С., Демин Д.С., Дмитриев А.В., Грачев Н.Е. Реализация метода решеточных уравнений Больцмана для расчетов на GPU-кластере // Вычислительные методы и программирование. 2012. 13. 13-19.
  10. Бикулов Д.А., Сенин Д.С. Реализация метода решеточных уравнений Больцмана без хранимых функций распределения для GPU // Вычислительные методы и программирование. 2013. 14. 370-374.
  11. Kupershtokh A.L. Three-dimensional LBE simulations of a decay of liquid dielectrics with a solute gas into the system of gas-vapor channels under the action of strong electric fields // Computers and Mathematics with Applications. 2014. 67, N 2. 340-349.
  12. Li W., Wei X., Kaufman A. Implementing lattice Boltzmann computation on graphics hardware // Visual Computer. 2003. 19, N 7/8. 444-456.
  13. Tölke J., Krafczyk M. TeraFLOP computing on a desktop PC with GPUs for 3D CFD // Int. J. Comput. Fluid Dyn. 2008. 22, N 7. 443-456.
  14. Obrecht C., Kuznik F., Tourancheau B., Roux J.-J. A new approach to the lattice Boltzmann method for graphics processing units // Computers and Mathematics with Applications. 2011. 61, N 12. 3628-3638.
  15. Walsh S.D. C., Saar M.O. Developing extensible lattice-Boltzmann simulators for general-purpose graphics-processing units // Commun. Comput. Phys. 2013. 13, N 3. 867-879.
  16. Alexander F.J., Chen S., Sterling J.D. Lattice Boltzmann thermohydrodynamics // Phys. Rev. E. 1993. 47, N 4. R2249-R2252.
  17. Qian Y.-H. Simulating thermohydrodynamics with lattice BGK models // Journal of Scientific Computing. 1993. 8, N 3. 231-242.
  18. Chen Y., Ohashi H., Akiyama M. Thermal lattice Bhatnagar-Gross-Krook model without nonlinear deviations in macrodynamical equations // Phys. Rev. E. 1994. 50, N 4. 2776-2783.
  19. Zhang R., Chen H. Lattice Boltzmann method for simulations of liquid-vapor thermal flows // Phys. Rev. E. 2003. 67, N 6. 066711-1-066711-6.
  20. Shan X. Simulation of Rayleigh-Bénard convection using a lattice Boltzmann method // Phys. Rev. E. 1997. 55, N 3. 2780-2788.
  21. He X., Chen S., Doolen G.D. A novel thermal model for the lattice Boltzmann method in incompressible limit // J. Comput. Phys. 1998. 146, N 2. 282-300.
  22. Guo Z., Zheng C., Shi B., Zhao T.S. Thermal lattice Boltzmann equation for low Mach number flows: decoupling model // Phys. Rev. E. 2007. 75, N 3. 036704-1-036704-15.
  23. Li Q., He Y.L., Wang Y., Tao W.Q. Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations // Phys. Rev. E. 2007. 76, N 5. 056705-1-056705-19.
  24. Qian Y.-H., d’Humiéres D., Lallemand P. Lattice BGK models for Navier-Stokes equation // Europhys. Lett. 1992. 17, N 6. 479-484.
  25. Lallemand P., Luo L.-S. Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance and stability // Phys. Rev. E. 2000. 61, N 6. 6546-6562.
  26. Koelman J.M. V.A. A simple lattice Boltzmann scheme for Navier-Stokes fluid flow // Europhys. Lett. 1991. 15, N 6. 603-607.
  27. Kupershtokh A.L. New method of incorporating a body force term into the lattice Boltzmann equation // Proc. 5th International EHD Workshop. Poitiers: University of Poitiers, 2004. 241-246.
  28. Куперштох А.Л. Учет действия объемных сил в решеточных уравнениях Больцмана // Вестник НГУ: Серия «Математика, механика и информатика». 2004. 4, № 2. 75-96.
  29. Kupershtokh A.L. Criterion of numerical instability of liquid state in LBE simulations // Computers and Mathematics with Applications. 2010. 59, N 7. 2236-2245.
  30. 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.
  31. Куперштох А.Л. Моделирование течений с границами раздела фаз жидкость-пар методом решеточных уравнений Больцмана // Вестник НГУ: Серия «Математика, механика и информатика». 2005. 5, № 3. 29-42.
  32. 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.
  33. 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.



How to Cite

Куперштох А.Л., Медведев Д.А., Грибанов И.И. Modeling of Thermal Flows in a Medium With Phase Transitions Using the Lattice Boltzmann Method // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2014. 15. 317-328



Section 1. Numerical methods and applications