Geodesic
Stability study of finite-difference-based lattice Boltzmann schemes with upwind differences of high order approximation
Numerical methods and programming, Tome 16 (2015) no. 2, pp. 196-204.

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The stability of three-level finite-difference-based lattice Boltzmann schemes of third and fourth orders of approximation with respect to spatial variables is studied. The stability analysis with respect to initial conditions is performed on the basis of a linear approximation. These studies are based on the Neumann method. It is shown that the stability of the schemes can be improved by the approximation convective terms in internal nodes of the grid stencils in use. In this case the stability domains are larger compared to the case of approximation in boundary nodes.
Keywords: lattice Boltzmann method, lattice Boltzmann schemes, stability with respect to initial conditions, Neumann method. 
@article{VMP_2015_16_2_a2,
     author = {G. V. Krivovichev and S. A. Mikheev},
     title = {Stability study of finite-difference-based lattice {Boltzmann} schemes with upwind differences of high order approximation},
     journal = {Numerical methods and programming},
     pages = {196--204},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2015_16_2_a2/}
}
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G. V. Krivovichev; S. A. Mikheev. Stability study of finite-difference-based lattice Boltzmann schemes with upwind differences of high order approximation. Numerical methods and programming, Tome 16 (2015) no. 2, pp. 196-204. http://geodesic.mathdoc.fr/item/VMP_2015_16_2_a2/