Abstract
In this paper we present a Lattice Boltzmann scheme for diffusion on it unstructured triangular grids. In this formulation of a LB for irregular grids there is no need for interpolation, which is required in other LB schemes on irregular grids. At the end of the propagation step the lattice gas particles arrive exactly at neighbouring lattice sites, as is the case in LB schemes on Bravais lattices. The scheme is constructed using the constraints that the moments of the equilibrium distribution equals that of the Maxwell-Boltzmann distribution. For a special choice of the relaxation parameter (ω = 1) we show that our LB scheme is identical to a cell centered Finite Volume scheme on an unstructured triangular grid.
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References
S. Chen and G.D. Doolen. Lattice Boltzmann method for fluid flows. Ann. Rev. Fluid Mech. 30: 329–364 (1998).
F. Nannelli and S. Succi. The Lattice Boltzmann-equation on irregular lattices. it J. Stat. Phys. 68(3–4): 401–407 (1992).
X. He, and G.D. Doolen, Lattice Boltzmann method on a curvilinear coordinate system: Vortex shedding behind a circular cylinder. Phys. Rev. E, 56, 430–440 (1997).
O. Filippova, and D. Haenel. Grid refinement for lattice-BGK models. J. Comput. Phys. 147, 219–228 (1998).
Van der Sman, R.G.M., and Ernst M.H., Convection Diffusion Lattice Boltzmann scheme for irregular Lattices, J. Comput. Phys., 160, 1–17 (2000).
R.G.M. van der Sman and M.H. Ernst. Gallilean invariant Convection-diffusion Lattice Boltzmann scheme for rectangular lattices. Phys. Rev. E, submitted (2003).
M. Junk. A Finite Difference Interpretation of the Lattice Boltzmann method. Numer. Methods Partial Differ. Eq., 17(4): 383–402 (2001).
D. Wolf-Gladrow. A Lattice Boltzmann equation for diffusion. J. Stat. Phys. 79(5/6): 1023–1032 (1995).
A. J. Chorin. A numerical method for solving incompressible viscous flow problems. J. Comput. Phys 2 12-(1967).
R. Herbin and O. Labergerie. Finite volume schemes for elliptic and elliptichyperbolic problems on triangular meshes Comp. Meth. Appl. Mech. Eng. 147(1–2): 85–103 (1997).
Van der Sman, R.G.M., and Ernst M.H., Diffusion Lattice Boltzmann scheme on an Orthorhombic Lattice, J. Stat. Phys., 94(1/2), (1999).
G. McNamara and B. Alder, Analysis of the Lattice Boltzmann treatment of hydrodynamics, Physica A, 194, 218–228, (1993).
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© 2003 Springer-Verlag Berlin Heidelberg
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van der Sman, R.G.M. (2003). Lattice Boltzmann Scheme for Diffusion on Triangular Grids. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Dongarra, J.J., Zomaya, A.Y., Gorbachev, Y.E. (eds) Computational Science — ICCS 2003. ICCS 2003. Lecture Notes in Computer Science, vol 2657. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44860-8_111
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DOI: https://doi.org/10.1007/3-540-44860-8_111
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