Geodesic
Stability analysis of the lattice Boltzmann schemes for solving the diffusion equation
Numerical methods and programming, Tome 14 (2013) no. 1, pp. 175-182.

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The one-parameter families of lattice Boltzmann schemes for solving the linear diffusion equation in the cases of D2Q5, D2Q7 and D2Q9 velocity sets are considered. The comparison of various schemes proposed in previous studies is performed. The stability analysis of schemes is performed in the space of parameters. The stability with respect to initial conditions is studied by the von Neumann method. The optimal parameter values for which the absolute values of the largest-in-magnitude eigenvalues of the transition matrix are minimal are found.
Keywords: lattice Boltzmann method; linear diffusion equation; stability with respect to initial conditions; von Neumann method. 
@article{VMP_2013_14_1_a20,
     author = {G. V. Krivovichev},
     title = {Stability analysis of the lattice {Boltzmann} schemes for solving the diffusion equation},
     journal = {Numerical methods and programming},
     pages = {175--182},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2013_14_1_a20/}
}
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G. V. Krivovichev. Stability analysis of the lattice Boltzmann schemes for solving the diffusion equation. Numerical methods and programming, Tome 14 (2013) no. 1, pp. 175-182. http://geodesic.mathdoc.fr/item/VMP_2013_14_1_a20/