Implementation of the lattice Boltzmann method without stored distribution functions on GPU

Authors

  • D.A. Bikulov Lomonosov Moscow State University
  • D.S.. Senin Lomonosov Moscow State University

Keywords:

computational fluid dynamics, high performance computing, graphics processing units

Abstract

A new algorithm for the lattice Boltzmann method optimized for GPU is proposed. The algorithm significantly reduces the DRAM memory amount required for operation in the 2D and 3D cases. A theoretical estimation of memory consumption is given. Numerical experiments confirm this theoretical estimate.

Author Biographies

D.A. Bikulov

D.S.. Senin

References

  1. Кривовичев Г.В. Об устойчивости решеточной кинетической схемы Больцмана для расчета плоских течений // Вычислительные методы и программирование. 2011. 12. 194-204.
  2. Кривовичев Г.В. Исследование устойчивости явных конечно-разностных решеточных кинетических схем Больцмана // Вычислительные методы и программирование. 2012. 13. 332-340.
  3. Куперштох А.Л. Трехмерное моделирование двухфазных систем типа жидкость-пар методом решеточных уравнений Больцмана на GPU // Вычислительные методы и программирование. 2012. 13. 130-138.
  4. Asinari P. Multiple-relaxation-time lattice Boltzmann scheme for homogeneous mixture flows with external force // Phys. Rev. E
  5. Bao J., Schaefer L. Lattice Boltzmann equation model for multi-component multi-phase flow with high density ratios // Applied Mathematical Modelling. 2012. 37, N 4. 1860-1871.
  6. Basit R., Basit M.A. Simulation of phase separation process using lattice Boltzmann method // Canadian J. on Computing in Mathematics, Natural Sciences, Engineering &; Medicine. 2010. 1, N 3. 71-76.
  7. Bhatnagar P.L., Gross E.P., Krook M. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems // Phys. Rev. 1954. N 94. 511-525.
  8. Kaehler G., Wagner A.J. Derivation of hydrodynamics for multi-relaxation time lattice Boltzmann using the moment approach // Computational Physics. 2013. 13, N 3. 614-628.
  9. Kao P.-H., Yang R.-J. An investigation into curved and moving boundary treatments in the lattice Boltzmann method // J. of Computational Physics. 2008. 227, N 11. 5671-5690.
  10. Latt J. How to implement your DdQq dynamics with only q variables per node (instead of 2q) // Technical Report. Medford: Tufts University, 2007.
  11. Mattila K., Hyväluoma J., Timonen J., Rossi T. Comparison of implementations of the lattice-Boltzmann method // Computers &; Mathematics with Applications. 2008. N 7. 1514-1524.
  12. McNamara G.R., Zanetti G. Use of the Boltzmann equation to simulate lattice-gas automata // Phys. Rev. Lett. 1988. 61. 2332-2335.
  13. Meldi M., Vergnault E., Sagaut P. An arbitrary Lagrangian-Eulerian approach for the simulation of immersed moving solids with lattice Boltzmann method // J. of Computational Physics. 2013. 235. 182-198.
  14. Narvaez A., Harting J. Evaluation of pressure boundary conditions for permeability calculations using the lattice Boltzmann method // Advances in Applied Mathematics and Mechanics. 2010. 2, N 5. 685-700.
  15. Obrecht C., Kuznik F., Tourancheau B., Roux J-J. Multi-GPU implementation of the lattice Boltzmann method // Computers &; Mathematics with Applications. 2013. 65, N 2. 252-261.
  16. Tölke J. Implementation of a lattice Boltzmann kernel using the Compute Unified Device Architecture developed by nVIDIA // Computing and Visualization in Science. 2010. 13, N 1. 29-39.
  17. Viggen E.M. The lattice Boltzmann method with applications in acoustics. Master’s Thesis. Trondheim: Norwegian Univ. of Science and Technology, 2009.
  18. Xian W., Takayuki A. Multi-GPU performance of incompressible flow computation by lattice Boltzmann method on GPU cluster // Parallel Computing. 2011. N 37. 521-535.
  19. Zou Q., He X. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model // Physics of Fluids. 1997. 9. 1591-1599.

Published

03-09-2013

How to Cite

Бикулов Д., Сенин Д. Implementation of the Lattice Boltzmann Method Without Stored Distribution Functions on GPU // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2013. 14. 370-374

Issue

Section

Section 1. Numerical methods and applications