Geodesic
Application of predictor-corrector finite-difference-based schemes in the lattice Boltzmann method
Numerical methods and programming, Tome 16 (2015) no. 1, pp. 10-17.

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Predictor-corrector finite-difference-based lattice Boltzmann schemes are proposed. An approach with separate approximation of spatial derivatives in the convective terms of kinetic equations and an approach when these terms are replaced by a single finite difference are considered. Explicit finite-difference schemes are used at both the stages of the computation process. The cavity flow problem and the Taylor vortex problem are solved numerically in a wide range of the Reynolds number. It is shown that the proposed schemes allow a larger time step compared to other known schemes.
Keywords: lattice Boltzmann method, kinetic equations, predictor-corrector, cavity flow problem, Taylor vortices. 
@article{VMP_2015_16_1_a1,
     author = {G. V. Krivovichev and E. V. Voskoboinikova},
     title = {Application of predictor-corrector finite-difference-based schemes in the lattice {Boltzmann} method},
     journal = {Numerical methods and programming},
     pages = {10--17},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2015_16_1_a1/}
}
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G. V. Krivovichev; E. V. Voskoboinikova. Application of predictor-corrector finite-difference-based schemes in the lattice Boltzmann method. Numerical methods and programming, Tome 16 (2015) no. 1, pp. 10-17. http://geodesic.mathdoc.fr/item/VMP_2015_16_1_a1/