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.

该贡献全面概述了非理想流体的格子玻尔兹曼模型，涵盖了动力学和宏观层面的理论概念以及数值性质的更实际讨论。在此背景下，详细介绍和讨论了理想气体动力学理论的要素。然后详细讨论了理想气体的格子玻尔兹曼方法从离散到伽利略不变性问题和不同的碰撞模型及其对流体动力学水平上的稳定性和一致性的影响。然后在气体动力学理论以及宏观层面的相应热力学（即范德华流体）的背景下引入对非理想流体的扩展，随后概述了基于不同晶格玻尔兹曼的非理想流体模型。