Large Eddy Simulation of the Lattice Boltzmann Equation for Turbulent Combustion

Book excerpt: The Lattice Boltzmann equation (LBE) was used to perform direct numerical simulations (DNS) and large-eddy simulations (LES) of benchmark problems in turbulence, scalar mixing, and reaction. The most important contribution was the development of LBE theory for binary mixing, which can be extended in a straight-forward manner to multi-scalar mixing. Computational simulations were performed to verify that the desired diffusive effects could be achieved in classical mixing problems. It was demonstrated that the shape of the probability density functions during binary mixing from non-premixed initial conditions was captured precisely. The technique for handling reactions in the LBE context also was demonstrated. In the standard one-dimensional flame propagation problem, the burning rate was captured accurately. The third significant contribution was the adaptation of the multi-time-scale relaxation technique to LES. Several DNS and LES calculations of benchmark turbulent flows (decaying isotropic and homogeneous shear, square jet) were performed to establish the effectiveness and efficiency of LBE. The decay exponent in decaying turbulence, the equilibrium anisotropies in homogeneous turbulence, and the spread rates in square jets were calculated accurately.