Geodesic
Approximation viscosity of one-parameter families of lattice Boltzmann equations
Numerical methods and programming, Tome 18 (2017) no. 1, pp. 41-52.

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A number of properties of parametric lattice Boltzmann schemes are considered. The Chapman-Enskog method is used to derive a system of equations for hydrodynamic variables and to obtain an expression for the approximation viscosity from the differential approximation of the schemes. It is shown that there exists the numerical viscosity that should be taken into account during numerical computations. Necessary stability conditions are obtained from the nonnegativity condition for the approximation viscosity. The possibility of computations using the proposed schemes is demonstrated by the numerical solution of the lid-driven cavity flow problem when the standard lattice Boltzmann equation is inapplicable.
Keywords: lattice Boltzmann method, approximation viscosity, stability. 
@article{VMP_2017_18_1_a3,
     author = {G. V. Krivovichev and E. A. Prokhorova},
     title = {Approximation viscosity of one-parameter families of lattice {Boltzmann} equations},
     journal = {Numerical methods and programming},
     pages = {41--52},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2017_18_1_a3/}
}
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G. V. Krivovichev; E. A. Prokhorova. Approximation viscosity of one-parameter families of lattice Boltzmann equations. Numerical methods and programming, Tome 18 (2017) no. 1, pp. 41-52. http://geodesic.mathdoc.fr/item/VMP_2017_18_1_a3/