Under-resolved and large eddy simulations of a decaying Taylor-Green vortex with the cumulant lattice Boltzmann method

We present a comprehensive analysis of the cumulant lattice Boltzmann model with the three-dimensional Taylor-Green vortex benchmark at Reynolds number 1600. The cumulant model is investigated in several different variants, using regularization, fourth-order convergent diffusion and fourth-order convergent advection with and without limiters. In addition, a cumulant model combined with a WALE sub-grid scale model is being evaluated. The turbulence model is found to filter out the high wave number contributions from the energy spectrum and the enstrophy, while the non-filtered cumulant methods show good correspondence to spectral simulations even for the high wave numbers. The application of the WALE turbulence model appears to be counter productive for the Taylor-Green vortex at a Reynolds number of 1600. At much higher Reynolds numbers (Re=160,000) a deviation from the ideal Kolmogorov theory can be observed in the absence of an explicit turbulence model. Cumulant models with fourth-order convergent diffusion show much better results than single relaxation time methods.

Automated summary

In this study, a comprehensive analysis of the cumulant lattice Boltzmann model with different variants was conducted on the three-dimensional Taylor-Green vortex at Reynolds number 1600. The findings show that cumulant models with fourth-order convergent diffusion perform better than single relaxation time methods, while the application of a cumulant model combined with a WALE turbulence model is not effective for the Taylor-Green vortex at a Reynolds number of 1600.