** Initial and boundary conditions for the lattice Boltzmann method **
*Phys. Rev. E, 48, 4823-4842*

This is probably the first article containing a systematic discussion on how to implement on-lattice boundary conditions in lattice Boltzmann using a finite difference scheme. The particle populations on the boundary are split into equilibrium and off-equilibrium part, and the results of the Chapman-Enskog expansion are used to associate off-equilbrium parts with velocity gradients. These gradient in their turn are evaluated by finite differences from the value of the velocity on neighboring nodes. It may take a while to get through this paper at a first reading, because the notation for the BGK model differs from the commonly used modern notation. However, the findings of the article remain valid and have been reused for different types of boundary conditions, including off-lattice boundaries.