Convection-Diffusion Lattice Boltzmann Scheme for Irregular Lattices |
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Authors: | R G M van der Sman M H Ernst |
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Institution: | Agrotechnological Research Institute, P.O. Box 17, Wageningen, NL-6700 AA, The Netherlandsf1;Institute for Theoretical Physics, University of Utrecht, Utrecht, The Netherlands, f2 |
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Abstract: | In this paper, a lattice Boltzmann (LB) scheme for convection diffusion on irregular lattices is presented, which is free of any interpolation or coarse graining step. The scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the Maxwell–Boltzmann distribution. The axioma holds for both Bravais and irregular lattices, implying a single framework for LB schemes for all lattice types. By solving benchmark problems we have shown that the scheme is indeed consistent with convection diffusion. Furthermore, we have compared the performance of the LB schemes with that of finite difference and finite element schemes. The comparison shows that the LB scheme has a similar performance as the one-step second-order Lax–Wendroff scheme: it has little numerical diffusion, but has a slight dispersion error. By changing the relaxation parameter ω the dispersion error can be balanced by a small increase of the numerical diffusion. |
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Keywords: | Abbreviations: lattice BoltzmannAbbreviations: convection diffusionAbbreviations: grid refinements |
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