Comparative Study of Boundary Conditions in LBM for Incompressible Laminar Flow

  • Alankar AgarwalEmail author
  • Akshay Prakash
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 308)


In this paper, we conduct a comparative study amongst different boundary conditions with two dimensional single-relaxation time lattice Boltzmann method (SRT-LBM), for incompressible laminar flow. Three types of boundary condition are considered for the simulation: including full-way bounce-back, half-way bounce-back, and modified bounce-back for the implementation of no-slip boundary condition on the wall with, pressure (density) boundary condition proposed by Zuo and He (Phys Fluids 9(6):1591–1598, 1997 [1]) for inlet/oulet. The benchmark fluid flow problem of steady plane Poiseuille’s flow with Reynolds number, Re = 75 is choosen. The numerical simulations are validated with the analytical solution, and grid convergence test are performed to compare accuracy of different boundary conditions.


Lattice Boltzmann method (LBM) Single-relaxation time Incompressible flow Boundary conditions 


  1. 1.
    Zou, Q., He, X.: On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys. Fluids 9(6), 1591–1598 (1997)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Chen, S., Doolen, G.D.: Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30(1), 329–364 (1998)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Gunstensen, A.K., Rothman, D.H.: Microscopic modeling of immiscible fluids in three dimensions by a lattice Boltzmann method. EPL (Europhys. Lett.) 18(2), 157 (1992)CrossRefGoogle Scholar
  4. 4.
    McClure, J.E., Prins, J.F., Miller, C.T.: Comparison of CPU and GPU implementations of the lattice Boltzmann method. In: XVIII International Conference on Water Resources, CMWR (2010)Google Scholar
  5. 5.
    Succi, S.: The Lattice Boltzmann Equation: for Fluid Dynamics and Beyond. Oxford University Press (2001)Google Scholar
  6. 6.
    Aidun, C.K., Clausen, J.R.: Lattice-Boltzmann method for complex flows. Annu. Rev. Fluid Mech. 42, 439–472 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Perumal, D.A., Dass, A.K.: A review on the development of lattice Boltzmann computation of macro fluid flows and heat transfer. Alexandria Eng. J. 54(4), 955–971 (2015)CrossRefGoogle Scholar
  8. 8.
    Mohammadipour, O.R., Niazmand, H., Succi, S.: General velocity, pressure, and initial condition for two-dimensional and three-dimensional lattice Boltzmann simulations. Phys. Rev. E 95(3), 033301 (2017)CrossRefGoogle Scholar
  9. 9.
    Kang, S.K., Hassan, Y.A.: A comparative study of direct-forcing immersed boundary-lattice Boltzmann methods for stationary complex boundaries. Int. J. Numer. Meth. Fluids 66(9), 1132–1158 (2011)CrossRefGoogle Scholar
  10. 10.
    Zhang, R., Chen, H.: Lattice Boltzmann method for simulations of liquid-vapor thermal flows. Phys. Rev. E 67(6), 066711 (2003)CrossRefGoogle Scholar
  11. 11.
    He, X., Luo, L.-S.: Lattice Boltzmann model for the incompressible Navier-Stokes equation. J. Stat. Phys. 88(3), 927–944 (1997)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Guo, Z., Shu, C.: Lattice Boltzmann Method and Its Applications in Engineering, vol. 3. World Scientific, Singapore (2013)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Indian Institute of Technology JodhpurJodhpurIndia
  2. 2.Indian Institute of Technology KharagpurKharagpurIndia

Personalised recommendations