Lattice Boltzmann for non-ideal fluids: Fundamentals and Practice

This contribution presents a comprehensive overview of lattice Boltzmann models for non-ideal fluids, covering both theoretical concepts at both kinetic and macroscopic levels and more practical discussion of numerical nature. In that context, elements of kinetic theory of ideal gases are presented and discussed at length. Then a detailed discussion of the lattice Boltzmann method for ideal gases from discretization to Galilean invariance issues and different collision models along with their effect on stability and consistency at the hydrodynamic level is presented. Extension to non-ideal fluids is then introduced in the context of the kinetic theory of gases along with the corresponding thermodynamics at the macroscopic level, i.e. the van der Waals fluid, followed by an overview of different lattice Boltzmann based models for non-ideal fluids. After an in-depth discussion of different well-known issues and artifacts and corresponding solutions, the article finishes with a brief discussion on most recent applications of such models and extensions proposed in the literature towards non-isothermal and multi-component flows.