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 ...