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 ($${\hbox {Re}}=160{,}000$$
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.
The simulation of fire is a challenging task due to its occurrence on multiple space-time scales and the non-linear interaction of multiple physical processes. Current state-of-the-art software such as the Fire Dynamics Simulator (FDS) implements most of the required physics, yet a significant drawback of this implementation is its limited scalability on modern massively parallel hardware. The current paper presents a massively parallel implementation of a Gas Kinetic Scheme (GKS) on General Purpose Graphics Processing Units (GPGPUs) as a potential alternative modeling and simulation approach. The implementation is validated for turbulent natural convection against experimental data. Subsequently, it is validated for two simulations of fire plumes, including a small-scale table top setup and a fire on the scale of a few meters. We show that the present GKS achieves comparable accuracy to the results obtained by FDS. Yet, due to the parallel efficiency on dedicated hardware, our GKS implementation delivers a reduction of wall-clock times of more than an order of magnitude. This paper demonstrates the potential of explicit local schemes in massively parallel environments for the simulation of fire.
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