Lattice Boltzmann methods for viscous fluid flows and for two-phase fluid flows

Lattice Boltzmann methods (LBMs) for viscous fluid flows and for two-phase fluid flows are presented. First, the LBMs for incompressible viscous fluid flows and for temperature fields are described. Then, we derive a lattice kinetic scheme (LKS) which is an improved scheme of the LBM. The LKS does not require any velocity distribution functions and is more stable than the LBMs. In addition, the LBM for two-phase fluid flows is presented. The method can simulate flows with the density ratio up to 1000. Numerical examples of unsteady flows in a three-dimensional porous structure, binary droplet collision and rising bubbles in a square duct are illustrated. It is expected that the LBMs (and LKS) will become promising numerical schemes for simulating complex fluid flows.