Geodesic
Stability of three-layer finite difference-based lattice Boltzmann schemes
Numerical methods and programming, Tome 15 (2014) no. 2, pp. 211-221.

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Stability of three-layer finite difference-based lattice Boltzmann schemes is studied. The time derivative is approximated by the central difference. The stability analysis with respect to initial conditions is performed. The Neumann method is used. It is shown that the stability of the schemes can be improved by the usage of averages of distribution function values on the nearest time layers. It is also shown that the usage of special approximations for the convective terms in the kinetic equations allows one to increase the stability domains in comparison with the case of the schemes with separate approximations of spatial derivatives.
Keywords: lattice Boltzmann method, lattice Boltzmann schemes, stability with respect to initial conditions, Neumann method. 
@article{VMP_2014_15_2_a2,
     author = {G. V. Krivovichev and S. A. Mikheev},
     title = {Stability of three-layer finite difference-based lattice {Boltzmann} schemes},
     journal = {Numerical methods and programming},
     pages = {211--221},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2014_15_2_a2/}
}
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G. V. Krivovichev; S. A. Mikheev. Stability of three-layer finite difference-based lattice Boltzmann schemes. Numerical methods and programming, Tome 15 (2014) no. 2, pp. 211-221. http://geodesic.mathdoc.fr/item/VMP_2014_15_2_a2/