Geodesic
Krivovichev G.V
Numerical methods and programming, Tome 13 (2012) no. 2, pp. 332-340.

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The stability problem is considered for finite difference-based lattice Boltzmann kinetic schemes for simulating the plane flows of a viscous incompressible isothermal fluid. Stability is studied for two steady modes of flow 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 demonstrated that the stability domains for a scheme with the first order upwind differences are included the maximum amount of points in a wide range of input parameters. It is shown for the case of equal time and space grid steps that the areas of the stability domains for the lattice Boltzmann equation are larger than for the cases of finite difference-based schemes.
Keywords: kinetic schemes; lattice Boltzmann equation; finite difference-based lattice Boltzmann schemes; stability with respect to initial conditions; Neumann method; stability domain. 
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     author = {G. V. Krivovichev},
     title = {Krivovichev {G.V}},
     journal = {Numerical methods and programming},
     pages = {332--340},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2012_13_2_a4/}
}
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G. V. Krivovichev. Krivovichev G.V. Numerical methods and programming, Tome 13 (2012) no. 2, pp. 332-340. http://geodesic.mathdoc.fr/item/VMP_2012_13_2_a4/