Abstract:
The lattice Boltzmann method-based large eddy simulation (LBM-LES), which is a new method to solve turbulence problems, has aroused widespread attention in recent decades. The Bhatnagar-Gross-Krook (BGK) approximation model, which is the most popular collision function for LBM, enables smooth recovery of the Navier-Stokes equation (NSE) from the lattice Boltzmann equation. However, the recovered NSE is compressible and employs additional terms related to the Mach (Ma) number. Thus, LBM-LES is inherently a pseudo-compressible method for solving the problem of incompressible fluids and generates the so-called “compressibility errors”. The compressibility errors include the deviations associated with the gradient of density and the deviations associated with Ma by the previous additional terms and velocity field divergence. In addition, in wind engineering, the collision step can exhibit the over-relaxation pattern, thus causing oscillation problems and degrading result accuracy, even though Ma and the gradient of density are not great. In this study, we discuss these errors by implementing an indoor isothermal forced convection benchmark case using the LBM-LES with the BGK model. The results indicate that different values of Ma that are controlled by the discrete time step δ in the LBM, affect the accuracy of the results significantly owing to compressibility errors. In particular, a large δ in coarse-grid resolutions produces obvious compressibility errors, while the errors can be compensated by scaling down δ. Meanwhile, an undersized δ leads to the turbulence fluctuations turning to numerical oscillations in the velocities owing to the over-relaxation of the distribution functions.
