Chikatamarla, S.S. and Karlin, I.V.
Lattices for the lattice Boltzmann method
Physical Review E, 79, (4), . (doi:10.1103/PhysRevE.79.046701).
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A recently introduced theory of higher-order lattice Boltzmann models [Chikatamarla and Karlin, Phys. Rev.
Lett. 97, 190601 (2006)] is elaborated in detail. A general theory of the construction of lattice Boltzmann
models as an approximation to the Boltzmann equation is presented. New lattices are found in all three
dimensions and are classified according to their accuracy (degree of approximation of the Boltzmann equation).
The numerical stability of these lattices is argued based on the entropy principle. The efficiency and accuracy
of many new lattices are demonstrated via simulations in all three dimensions.
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