Derivation of Multicomponent Lattice Boltzmann Equations by Introducing a Nonequilibrium Distribution Function into the Maxwell Iteration Based on the Convective Scaling

• Published in: Journal of statistical physics 2021, Vol.182 (1), Article 4
• Main Authors: Yamamoto, Keiichi, Seta, Takeshi
• Format: Article
• Language: English
• Subjects: Analysis; Distribution (Probability theory); Distribution functions; Iterative methods; Kinetic equations; Mathematical and Computational Physics; Maxwell's equations; Physical Chemistry; Physics; Physics and Astronomy; Quantum Physics; Recursive methods; Statistical Physics and Dynamical Systems; Theoretical; Velocity distribution
• ISSN: 0022-4715; 1572-9613
• DOI: 10.1007/s10955-020-02686-x

This study firstly proposes a simple recursive method for deriving the macroscale equations from lattice Boltzmann equations. Similar to the Maxwell iteration based on the convective scaling, this method is used to expand the lattice Boltzmann (LB) equations with the time step δ t . It is characterised by the incorporation of a nonequilibrium distribution function not appearing in the Maxwell iteration to considerably reduce the mathematical manipulations required. Next, we define the kinetic equations of a multicomponent (i.e. N-component) system based on a model using the Maxwell velocity distribution law for the equilibrium distribution function appearing in the cross-collision terms. Then, using this simple recursive method, we derive the generalized Stefan–Maxwell equation, which is the macroscale governing equation of a multicomponent system while ensuring the mass conservation. In short, our objective is to firstly define the kinetic equations of a multi-component system having a clear physical interpretation and then formulate the LB equations of any N-component system deductively.