On the small-scale dynamical behavior of lattice BGK and lattice Boltzmann schemes

Abstract

In this paper, we report some comparative simulations between lattice BGK and lattice Bolzmann schemes for two-dimensional fluid flows. A quantitative assessment of the validity of the lattice BGK and lattice Bolzmann schemes is presented for the two-dimensional weakly compressibleKolmogorov flow. We use this flow to study the difference of the two schemes at small scales. A lowReynolds (R e ∼ 300) number simulation shows the almost identical energy spectra for both schemes except for the small-scale dynamics of lattice Bolzmann which is more noisy. Because of the intrinsic difficulties of nonlinear stability analysis, we use numerical simulations to investigate which scheme is more stable. It turns out the lattice BGK is more stable. It turns out the lattice BGK is more robust than lattice Bolzmann by increasing theReynolds numbers. Detailed comparison with other methods (e.g., spectral method) remains to be done in the near future.