The lattice Boltzmann advection-diffusion model revisited

@article{Chopard2009TheLB,
  title={The lattice Boltzmann advection-diffusion model revisited},
  author={Bastien Chopard and Jean-Luc Falcone and Jonas Latt},
  journal={The European Physical Journal Special Topics},
  year={2009},
  volume={171},
  pages={245-249}
}
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. 

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