The molecular dynamics lattice gas (MDLG) method maps a molecular dynamics (MD) simulation onto a lattice gas using a coarse-graining procedure. This is a novel fundamental approach to derive the lattice Boltzmann method (LBM) by taking a Boltzmann average over the MDLG. A key property of the LBM is the equilibrium distribution function, which was originally derived by assuming that the particle displacements in the MD simulation are Boltzmann distributed. However, we recently discovered that a single Gaussian distribution function is not sufficient to describe the particle displacements in a broad transition regime between free particles and particles undergoing many collisions in one time step. In a recent publication, we proposed a Poisson weighted sum of Gaussians which shows better agreement with the MD data. We derive a lattice Boltzmann equilibrium distribution function from the Poisson weighted sum of Gaussians model and compare it to a measured equilibrium distribution function from MD data and to an analytical approximation of the equilibrium distribution function from a single Gaussian probability distribution function.

This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

分子动力学晶格气体 (MDLG) 方法使用粗粒度程序将分子动力学 (MD) 模拟映射到晶格气体上。这是通过在 MDLG 上取玻尔兹曼平均值来推导晶格玻尔兹曼方法 (LBM) 的一种新颖的基本方法。LBM 的一个关键特性是平衡分布函数，它最初是通过假设 MD 模拟中的粒子位移是 Boltzmann 分布而导出的。然而，我们最近发现单个高斯分布函数不足以描述自由粒子和在一个时间步长内经历多次碰撞的粒子之间的广泛过渡区域中的粒子位移。在最近的一篇文章中，我们提出了高斯的泊松加权和，它与 MD 数据显示出更好的一致性。

本文是主题问题“流体动力学模拟中尺度方法的进展”的一部分。