Anomaly of the lattice Boltzmann methods in three-dimensional cylindrical flows

Truncation error terms of the lattice Boltzmann equation (LBE) are analysed for three-dimensional flow simulations by the D3Q15, D3Q19 and D3Q27 models. By applying the analysis of Holdych et al. (2004) [9], rotational invariance of the Reynolds averaged error terms is examined in cylindrical coordinates. It is found that error terms distribute cyclically in the circumferential direction and produce false forces in particular directions by the D3Q15 and D3Q19 models. When flow becomes turbulent, this tendency is reinforced by the Reynolds stress resulting in the generation of obvious spurious currents. By the D3Q27 model, it is confirmed that the LBE keeps rotational invariance in laminar flows whilst non-axisymmetric error terms arise in turbulent flows. However, the magnitudes of the error terms are less than two percent of those by the D3Q15 and D3Q19 models and hence unphysical spurious currents are sufficiently weak.