Predictor-corrector finite-difference lattice Boltzmann schemes

Abstract

Predictor-corrector finite-difference lattice Boltzmann schemes are proposed. An approach with separate approximation of spatial derivatives in the advective term of kinetic equations and an approach when this term is replaced by a single finite difference are considered. Explicit finite-difference schemes are used at both the stages of the computation process. The lid-driven cavity flow problem and the Taylor — Green 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 well-known upwind schemes. Mathematics Subject Classification: 76-04; 76M10; 65N30