Self-consistent Force Scheme in the Discrete Boltzmann Equation

TL;DR

This paper develops a self-consistent force scheme for the Discrete Boltzmann Equation using Hermite basis expansions with various velocity scalings, extending previous models and deriving new force schemes.

Contribution

It introduces a new force scheme based on Hermite basis with scaled velocity, expanding the theoretical framework for force implementation in the Discrete Boltzmann Equation.

Findings

Derived force scheme using Hermite basis with relative velocity in comoving coordinates.

Showed the existing scheme by He et al. can be derived from Hermite basis with relative velocity.

Proposed a novel force scheme with velocity scaled by local temperature.

Abstract

In the work of N. Martys et al. [Nicos S. Martys, Xiaowen Shan, Hudong Chen, Phys. Rev. E, Vol. 58, Num.5, 1998 ], a self-consistent force term to any order in the Boltzmann-BKG equation is derived by the Hermite basis with raw velocity. As an extension, in the present work, the force term is expanded by the Hermite basis with the relative velocity in the comoving coordinate and the Hermite basis with the relative velocity scaled by the local temperature. It is found that the force scheme proposed by He et al. [Xiaoyi He, Xiaowen Shan, Gary D. Doolen, Phys. Rev. E, Vol. 57, Num.1,1998] can be derived by the Hermite basis with the relative velocity. Furthermore, another new force scheme in which the velocity is scaled by the local temperature is obtained.