Numerical illustrations of the coupling between the lattice boltzmann method and finite-type macro-numerical methods

An analytic expression called a reconstruction operator is proposed for the exchange from velocity of finite-type methods to the single-particle distribution function of the lattice Boltzmann method (LBM). The combined finite-volume method and lattice Boltzmann method (called the CFVLBM) is adopted to solve three flow cases, backward-facing flow, flow around a circular cylinder, and lid-driven cavity flow. The results predicted by the CFVLBM agree with the available numerical solutions very well. It is shown that the vorticity contour distribution is a more appropriate parameter to ensure good smoothness and consistency at the coupling interface. At the same time, CPU time used by the CFVLBM(II), with more than one outer iteration before interface information exchange, is much less than that of the CFVLBM(I), where interface information exchanges are executed after each outer iteration.