PREFACE: LATTICE BOLTZMANN METHOD

of the Lattice Boltzmann Method for Numerical Simulations of Multiphase Flows. the Lattice Boltzmann applied to a variety of numerical calculations for turbulence, particulate flows, multi-component mixtures, and multiphase flows. Approximately three ago, the Lattice Boltzmann Method pro-posed as a descendant of the Lattice gas cellular automata, which consists of the propagation and collision processes of particles. In this method, the distribution functions take the place of the particles to recover the Navier-Stokes equations exactly. Mutually independent dynamics of the distribution functions along the lattices are compatible with parallel computing and easy treat-ment of complicated geometries. Although the fast computation and simple algorithm attracted much attention from researchers in the computational fluid dynamics field, the primary Lattice Boltzmann Methods were numerically unstable in the simulation of the multiphase flows that have high-density ratios and high Reynolds numbers. The most advanced Lattice Boltzmann Methods successfully calculate multiphase flows with a high-density ratio at a high Reynolds number without the inherent problems, such as numerical instability and spurious current on the liquid–vapor interface. These models have already been used in commercial software world-wide. With the opportunity to publish this special issue on the Lattice Boltzmann Method, we hope that this issue will be helpful for further development of the Lattice Boltzmann Method for multiphase flows.