Abstract
In the last decade or so, the Lattice–Boltzmann method (LBM) has achieved great success in computational fluid dynamics. The Fully–Lagrangian method (FLM) is the generalization of LBM for conservation systems. LBM can also be developed from FLM. In this paper a FL model and a LB model are developed for D-dimensional advection-diffusion equation. The LB model can be viewed as an improved version of the FL model. Numerical results of simulation of 1-dimensional advection-diffusion equation are presented. The numerical results are found to be in good agreement with the analytic solution.
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REFERENCES
Ancona, G. M. (1994). Fully Lagrangian and Lattice-Boltzmann Methods for Solving Systems of Conservation Equations. J. Comp. Phys. 115, 107–120.
Chen, S., and Doolen, G. D. (1998). Lattice Boltzmann Method for Fluid Flows. Ann. Rev. Fluid Mech. 30, 329–364.
Cornubert, R., d'Humieres, D., and Levermore, D. (1991). A Knudsen layer theory for lattice gases. Physica D 47, 241–259.
Nobel, D. R., Chen, S., Georgiadis, J. D., and Buckius, R. O. (1995). A consistent hydrodynamics boundary condition for the lattice Boltzmann method. Phys. Fluids. 7, 203–209.
Chen, S., Martinez, D., and Mei, R. (1996). On boundary condition in lattice Boltzmann methods. Phys. Fluids. 8, 2527–2536.
Wolf-Gladrow, D. (1995). A Lattice Boltzmann Equation for Diffusion. J. Stat. Phys. 79, 1023–1031.
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Guo, Z.L., Shi, B.C. & Wang, N.C. Fully Lagrangian and Lattice Boltzmann Methods for the Advection-Diffusion Equation. Journal of Scientific Computing 14, 291–300 (1999). https://doi.org/10.1023/A:1023273603637
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DOI: https://doi.org/10.1023/A:1023273603637