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 $$\delta _{t}$$ 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.

中文翻译：

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基于对流标度的麦克斯韦迭代引入非平衡分布函数推导多分量格子玻尔兹曼方程

本研究首先提出了一种简单的递归方法，用于从格子 Boltzmann 方程导出宏观方程。类似于基于对流缩放的麦克斯韦迭代，该方法用于以时间步长$$\delta _{t}$$ δ t 扩展格子玻尔兹曼（LB）方程。它的特点是结合了麦克斯韦迭代中没有出现的非平衡分布函数，以大大减少所需的数学运算。接下来，我们基于一个模型定义多组分（即 N 组分）系统的动力学方程，该模型使用麦克斯韦速度分布定律作为出现在交叉碰撞项中的平衡分布函数。然后，使用这种简单的递归方法，我们推导出广义的 Stefan-Maxwell 方程，这是多组分系统在保证质量守恒的情况下的宏观控制方程。简而言之，我们的目标是首先定义一个具有明确物理解释的多组分系统的动力学方程，然后推导出任何 N 组分系统的 LB 方程。