Three-dimensional LBE simulations on hybrid GPU-clusters for the decay of a binary mixture of liquid dielectrics with a solute gas to a system of gas-vapor channels


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


lattice Boltzmann equation method, phase transitions, dynamics of multiphase media, binary mixtures, breakdown of dielectric liquids, computer simulations, parallel computing, graphics processing units, hybrid supercomputers


In the lattice Boltzmann equation method (LBE), 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 included in modern Graphics Processing Units (GPU). Hybrid GPU-clusters allows us to exploit a new level of simulations of multi-physic problems. The 3D simulations of a spinodal decomposition were carried out on grids consisting of more than 250 million nodes. The 3D simulations of the anisotropic decay of binary mixtures of dielectric liquids with a solute gas under a strong electric field to a system of gas-vapor channels in a liquid that are parallel to the local electric field is performed. The gas-vapor channels expand because of the diffusion of a solute gas and due to a process of coalescence. The critical value of the uniform electric field decreases with an increase in the initial concentration of a solute gas. This indicates that such an electrostrictive mechanism of the generation, growth and branching of the channels during the breakdown of real dielectric liquids in the nanosecond range is possible.

Author Biography

A.L. Kupershtokh


  1. Kupershtokh A.L., Medvedev D.A. Anisotropic instability of a dielectric liquid in a strong uniform electric field: decay into a two-phase system of vapor filaments in a liquid // Phys. Rev. E. 2006. 74, N 2. 021505.
  2. Карпов Д.И., Куперштох А.Л. Анизотропный спинодальный распад полярного диэлектрика в сильном электрическом поле: метод молекулярной динамики // Письма в ЖТФ. 2009. 35, вып. 10. 87-94.
  3. An W., Baumung K., Bluhm H. Underwater streamer propagation analyzed from detailed measurements of pressure release // J. Appl. Phys. 2007. 101, N 5. 053302.
  4. Kupershtokh A.L., Karpov D.I. Simulation of ultra-fast streamer growth governed by the mechanism of anisotropic decay of a dielectric liquid into a liquid-vapor system in high electric fields // Proc. 5th Conf. SFE. Grenoble, France. 2006. 179-184.
  5. 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.
  6. 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.
  7. Kupershtokh A.L. Criterion of numerical instability of liquid state in LBE simulations // Computers and Mathematics with Applications. 2010. 59, N 7. 2236-2245.
  8. Куперштох А.Л. Трехмерное моделирование двухфазных систем типа жидкость-пар методом решеточных уравнений Больцмана на GPU // Вычислительные методы и программирование. 2012. 13, № 1. 130-138.
  9. 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.
  10. Qian Y.H., Chen S. Finite size effect in lattice-BGK models // Int. J. of Modern Physics C. 1997. 8, N 4. 763-771.
  11. Kupershtokh A.L., Karpov D.I., Medvedev D.A., Stamatelatos C., Charalambakos V.P., Pyrgioti E.C., Agoris D.P. Stochastic models of partial discharge activity in solid and liquid dielectrics // IET Sci. Meas. Technol. 2007. 1, N 6. 303-311.
  12. Kupershtokh A.L. New method of incorporating a body force term into the lattice Boltzmann equation // Proc. of the 5th International EHD. Workshop, Poitiers, France. 2004. 241-246.
  13. Куперштох А.Л. Учет действия объемных сил в решеточных уравнениях Больцмана // Вестник НГУ. Серия «Математика, механика и информатика». 2004. 4, № 2. 75-96.
  14. NVIDIA CUDA C. Programming Guide. Version 4.0. 2011.
  15. NVIDIA CUDA C. Programming Guide. Version 4.2. 2012.
  16. 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, № 1. 13-19.
  17. Obrecht C., Kuznik F., Tourancheau B., Roux J.-J. Multi-GPU implementation of the lattice Boltzmann method // Computers and Mathematics with Applications. 2012.
    doi 10.1016/j.camwa.2011.02.020
  18. Ландау Л.Д., Лифшиц Е.М. Электродинамика сплошных сред. М.: Гос. изд-во физ.-мат. литературы, 1959.



How to Cite

Куперштох А. Three-Dimensional LBE Simulations on Hybrid GPU-Clusters for the Decay of a Binary Mixture of Liquid Dielectrics With a Solute Gas to a System of Gas-Vapor Channels // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2012. 13. 384-390



Section 1. Numerical methods and applications