Subgrid-scale model derived from the lattice Boltzmann equation

The cumulant lattice Boltzmann method (LBM), a variant of LBM, inherently exhibits an implicit large-eddy simulation (LES) effect. To facilitate subgrid-scale (SGS) turbulence modeling, we analyze the error terms of the lattice Boltzmann equation and deductively derive a novel, parameter-free SGS model (hereafter the kinetic model). A priori tests using direct numerical simulation (DNS) data were conducted for both the absolute magnitude of the SGS volume force and the SGS dissipation. These tests show that, while the gradient model (GM) performs slightly better in terms of local correlation and mean absolute error, the kinetic model (KM) provides closer agreement with DNS in the global distribution and large-scale coherence of the SGS fields. In this sense, the KM demonstrates superior capability for capturing the overall structure of turbulent energy transfer. In addition, a posteriori validation using LESs of the Taylor–Green vortex confirms that the KM reproduces the dissipation rate and energy spectra more accurately than the GM while maintaining numerical stability. Thus, the present study evaluates the model both a priori and a posteriori, confirming its effectiveness and robustness.