Applications of the lattice Boltzmann method to complex and turbulent flows

Abstract. We brie y review the mathematics of the lattice Boltzmann equation, and show the direct numerical simulations of non-spherical particulate suspensions in uid ows and three-dimensional homogeneous isotropic turbulence ow in a periodic cubic box of the size 128 3. We compare the LBE simulation of the homo-geneous isotropic turbulence ow with the pseudo-spectral simulation. We observed that the lattice Boltzmann method is easy to implement on massively parallel com-puters and its computational speed scales linearly with the number of the CPUs.