Systematic evaluation of stencil configuration, forcing scheme, and resolution effects in the stratified Taylor–Green vortex: A lattice Boltzmann study

The rigorous simulation of stratified turbulence remains challenging due to pronounced flow anisotropy, suppressed vertical transport, and high sensitivity to numerical dissipation. This study systematically evaluates the predictive capability of the lattice Boltzmann method (LBM) for a three-dimensional stratified Taylor–Green vortex. Within a double-distribution-function framework under the Boussinesq approximation, we examine the influence of stencil configurations, forcing formulations, and spatial resolutions up to 2563, with validation against spectral direct numerical simulation benchmarks. The results demonstrate that the D3Q27×19 configuration achieves an optimal balance between numerical accuracy and computational efficiency, accurately reproducing the temporal evolution of kinetic and potential energies as well as the characteristic double-peak dissipation structure. Grid-sensitivity analysis further reveals that potential energy and fine-scale turbulent structures are significantly more resolution-dependent than kinetic energy, requiring a minimum resolution of 2563 for quantitative convergence. Moreover, under strongly stratified conditions, the velocity-shift forcing schemes outperform discrete source-term approaches, reducing the overall error by approximately 45.33%. Finally, a symmetry-breaking velocity-error diagnostic shows that the previously used D3Q27×7 configuration, despite reasonable global energy predictions, accumulates substantially larger hidden symmetry errors than D3Q27×19 under strong stratification. Overall, this work provides practical guidelines for high-fidelity LBM simulations of stratified turbulence and highlights that the coordinated selection of stencil isotropy, spatial resolution, force discretization, and symmetry preservation is essential for accurately capturing energy cascade and mixing dynamics.