Systematic Evaluation of Stencil Configuration, Forcing Scheme, and Resolution Effects in the Stratified Taylor--Green Vortex: A Lattice Boltzmann Study

TL;DR

This paper systematically evaluates the lattice Boltzmann method's accuracy in simulating stratified turbulence, focusing on stencil configurations, forcing schemes, and resolution, validated against spectral DNS benchmarks.

Contribution

It identifies optimal LBM configurations and resolution requirements for accurate stratified turbulence simulation, providing practical guidelines for high-fidelity modeling.

Findings

D3Q27×19 configuration balances accuracy and efficiency

Potential energy and small-scale structures are more resolution-dependent

Velocity-shift forcing schemes reduce error by ~45.54% under stratification

Abstract

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 $256^3$, with validation against spectral DNS benchmarks. The results demonstrate that the D3Q27$\times$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 $256^3$ for quantitative convergence. Moreover, under strongly stratified conditions, the velocity-shift forcing schemes outperform discrete source-term approaches, reducing the overall error by approximately 45.54\%. 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, and force discretization is essential for accurately capturing energy cascade and mixing dynamics.