The lattice Boltzmann advection-diffusion model revisited
Advection-diffusion processes can be simulated by the Lattice Boltzmann method. Two formulations have been proposed in the literature. We show that they are not fully correct (only first order accurate). A new formulation is proposed, which is shown to produce better results, both from the point of view of the Chapman-Enskog expansion or when comparing simulations with an exact time-dependent solution of the advection-diffusion equation.
KeywordsEuropean Physical Journal Special Topic Lattice Boltzmann Method Lattice Boltzmann Lattice Boltzmann Equation Lattice Boltzmann Simulation
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- S. Succi, The Lattice Boltzmann Equation, For Fluid Dynamics and Beyond (Oxford University Press, 2001)Google Scholar
- B. Chopard, M. Droz, Cellular Automata Modeling of Physical Systems (Cambridge University Press, 1998)Google Scholar
- E.G. Flekkoy, Phys. Rev. E 47, 4247 (1993)Google Scholar
- Z.L Guo, B.C. Shi, N.C. Wang, J. Scient. Comp. 14, 291 (1999)Google Scholar
- S. Suga, Int. J. Mod. Phys. C 17, 1563 (2006)Google Scholar
- R.G.M. Van der Sman, M.H. Ernst, J. Comp. Phys. 160, 766 (2000)Google Scholar
- A. Wagner (private communication)Google Scholar
- B. Shi, Lattice Boltzmann simulation of some nonlinear complex equations, Computanional Science ICCS 2007, vol. 4487 of LNCS (Springer Berlin, Heidelberg, 2007), p. 818Google Scholar
- J. Lätt, Hydrodynamic Limit of Lattice Boltzmann equations, Ph.D. thesis, University of Geneva, Switzerland, 2007 http://www.unige.ch/cyberdocuments/theses2007/LattJ/meta.html Google Scholar