Lattice Boltzmann for non-ideal fluids: Fundamentals and Practice

TL;DR

This paper provides a comprehensive overview of lattice Boltzmann models for non-ideal fluids, covering theoretical foundations, numerical methods, extensions, issues, solutions, and recent applications in complex flow simulations.

Contribution

It offers an in-depth synthesis of lattice Boltzmann methods for non-ideal fluids, integrating kinetic theory, thermodynamics, and practical modeling extensions.

Findings

Discussion of stability and consistency issues in lattice Boltzmann models.

Overview of solutions to artifacts and modeling challenges.

Recent applications to non-isothermal and multi-component flows.

Abstract

This contribution presents a comprehensive overview of 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.