ALattice boltzmann method for the advection-diffusion equation with neumann boundary conditions

Communications in Computational Physics

Volumn 15, Issue 2, 2014, Pages 487-505

  Gebäck, Tobias ^a   Heintz, Alexei ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Advection diffusion; Diffusion; Lattice Boltzmann; Neumann boundary condition

Indexed keywords

EID: 84887808984     PISSN: 18152406     EISSN: 19917120     Source Type: Journal    
DOI: 10.4208/cicp.161112.230713a     Document Type: Article

References (19)

1. A. Caiazzo. Analysis of lattice boltzmann initialization routines. J. Stat. Phys., 121(1-2):37-48, 2005. (Pubitemid 41660269)
2. H. Chen, S. Chen, and W. H. Matthaeus. Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. Phys. Rev. A, 45:R5339-R5342, 1992.
3. S. Chen and G. D. Doolen. Lattice Boltzmannmethod for fluid flows. Ann. Rev. FluidMech., 30:329-364, 1998.
4. S. Y. Chen, Z. Wang, X. Shan, and G. D. Doolen. Lattice Boltzmann computational fluid dynamics in three dimensions. J. Stat. Phys., 68(3-4):379-400, 1992. Advanced Research Workshop on Lattice Gas Automata (Nice, 1991).
5. M. Geier, A. Greiner, and J. G. Korvink. Bubble functions for the lattice Boltzmann method and their application to grid refinement. Eur. Phys. J.-Special Topics, 171:173-179, 2009.
6. I. Ginzburg. Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation. Adv.Water Resour., 28(11):1171-1195, 2005. (Pubitemid 41448126)
7. I. Ginzburg. Generic boundary conditions for lattice Boltzmann models and their application to advection and anisotropic dispersion equations. Adv. Water Resour., 28(11):1196-1216, 2005. (Pubitemid 41448127)
8. I. Ginzburg, F. Verhaeghe, and D. d'Humieres. Two-relaxation-time lattice Boltzmann scheme: About parametrization, velocity, pressure and mixed boundary conditions. Commun. Comp. Phys., 3(2):427-478, 2008.
9. F. J. Higuera, S. Succi, and R. Benzi. Lattice gas dynamics with enhanced collisions. Europhys. Lett., 9(4):345, 1989.
10. A. Hiorth, U. H. A. Lad, S. Evje, and S.M. Skjaeveland. A lattice Boltzmann-BGK algorithm for a diffusion equation with Robin boundary condition-application to NMR relaxation. Int. J. Numer. Meth. Fluids, 59(4):405-421, 2009.
11. H.-B. Huang, X.-Y. Lu, and M. C. Sukop. Numerical study of lattice Boltzmann methods for a convection-diffusion equation coupled with Navier-Stokes equations. J. Phys. A, 44(5):055001, 2011.
12. M. Junk, A. Klar, and L.-S. Luo. Asymptotic analysis of the lattice Boltzmann equation. J. Comp. Phys., 210:676-704, 2005. (Pubitemid 41179665)
13. Q. Kang. Simulation of dissolution and precipitation in porous media. J. Geophys. Res., 108(B10):1-10, 2003.
14. K. Moriyama and T. Inamuro. Lattice boltzmann simulations of water transport from the gas diffusion layer to the gas channel in pefc. Commun. Comp. Phys., 9:1206-1218, 2011.
15. A. S. Sangani and A. Acrivos. The effective conductivity of a periodic array of spheres. Proc. R. Soc. A, 386(1791):263-275, 1983. (Pubitemid 13521227)
16. M. Stiebler, J. Tölke, and M. Krafczyk. Advection-diffusion lattice Boltzmann scheme for hierarchical grids. Comput. Math. Appl., 55(7):1576-1584, 2008. (Pubitemid 351273560)
17. F. Verhaeghe, S. Arnout, B. Blanpain, and P.Wollants. Lattice-Boltzmann modeling of dissolution phenomena. Phys. Rev. E, 73(3):036316, 2006.
18. H. Yoshida and M. Nagaoka. Multiple-relaxation-time lattice Boltzmann model for the convection and anisotropic diffusion equation. J. Comp. Phys., 229(20):7774-7795, 2010.
19. X. X. Zhang, J. W. Crawford, A. G. Bengough, and I. M. Young. On boundary conditions in the lattice Boltzmann model for advection and anisotropic dispersion equation. Adv.Water Resour., 25(6):601-609, 2002.