7 - Practice of Lattice Boltzmann Simulations

Abstract

This chapter analyzes the lattice Boltzmann method, which is generally used as a simulation technique for a pure liquid system but has a different approach to the molecular simulation and microsimulation methods. The method is a potential simulation technique for taking into account multibody hydrodynamic interactions among particles in a particle suspension or polymers in a polymeric liquid. In treating fluid properties, such as the flow field, the method employs an abstract approach that makes use of the particle distribution function, whereas the usual fluid simulation method deals with quantities that are intuitively understandable, such as velocities and pressures. The concept of the particle distribution function and the theoretical background of this simulation method will enable the application of the method to various types of flow problems in a relatively straightforward manner. An exercise is provided to address a uniform flow around a circular cylinder, which will be a foundation for applying the method to flow problems in particle dispersion or a polymeric liquid. The validity of the solution obtained by this method can be evaluated by comparing it with that obtained by a fully developed simulation method, such as the finite difference method. The sample simulation program has been developed from the viewpoint of applying it to a particle suspension; it may thus be very valuable in a practical context.