Impact of reconstruction schemes on interpreting lattice Boltzmann results -- A study using the Taylor-Green vortex problem

In this note, we show how reconstruction schemes can have a significant impact on interpreting lattice Boltzmann simulation data. To reconstruct turbulence quantities, e.g., the kinetic energy dissipation rate and enstrophy, schemes higher than second-order for spatial derivatives can greatly improve the prediction of these quantities in the Taylor-Green vortex problem. In contrast, a second-order reconstruction of the time series data indicates very good accuracy for the kinetic energy dissipation rate. The present findings can be considered as further numerical evidence of the capability of the lattice Boltzmann method to simulate turbulent flows, which is consistent with its proven feature of low numerical diffusion.
Comment: 12 pages, 4 figures, 5 tables