Geodesic
Stability of finite-difference-based lattice Boltzmann schemes
Numerical methods and programming, Tome 14 (2013) no. 1, pp. 1-8.

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The stability of finite-difference-based lattice Boltzmann schemes is studied on the basis of a special approach to the finite-difference approximation of kinetic equations. The derivatives with respect to the space variables are not approximated separately, but the entire term containing these derivatives is approximated. Three different finite-difference-based schemes are considered. The stability is analyzed in the cases of two stationary flow regimes in an unbounded domain. The stability analysis is performed with respect to initial conditions using the Neumann method in a linear approximation. A number of stability domains are constructed and studied in the space of input parameters. It is shown that the schemes under consideration are conditionally stable. It is also shown that the stability domains for these schemes are larger than the domains for the schemes based on the separate approximation of the spatial derivatives.
Keywords: lattice Boltzmann method, finite-difference-based lattice Boltzmann schemes, stability with respect to initial conditions, Neumann method, stability domain. 
@article{VMP_2013_14_1_a0,
     author = {G. V. Krivovichev},
     title = {Stability of finite-difference-based lattice {Boltzmann} schemes},
     journal = {Numerical methods and programming},
     pages = {1--8},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2013_14_1_a0/}
}
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G. V. Krivovichev. Stability of finite-difference-based lattice Boltzmann schemes. Numerical methods and programming, Tome 14 (2013) no. 1, pp. 1-8. http://geodesic.mathdoc.fr/item/VMP_2013_14_1_a0/