Novel Multi-relaxation-time High-order Models for Lattice Boltzmann Simulation of Non-equilibrium Gas Flows

微/纳米流体技术与微/纳米机电系统和微总量分析系统相关联，旨在彻底改变化学，制药和食品工业。流动模拟在这些小型化设备的设计中至关重要，但在预测微/纳米尺度的气体流动行为时存在一个主要问题。当气体分子的平均自由程与器件的特征维数相当时，违反了Navier-Stokes-Fourier （NSF）方程所依赖的热力学准平衡假设。当标准的连续体NSF方程失效时，整个流场模拟的分子动力学方法超出了当前的计算能力。我们提出了一种介观晶格玻尔兹曼（LB）方法来填补连续统和分子方法之间的空白，旨在为非平衡气体流动提供定量准确的结果，但只需要分子动力学方法的一小部分计算成本。除了开发等温和热非平衡流的高阶介观LB模型外，我们还将提出多种松弛时间方案，以解决不同阶速度矩（包括动量和能量）的不同松弛率。对于热流，在平衡分布函数的Hermite展开近似中，不再寻求大的离散速度集来保留高达5阶的速度项，而是引入额外的能量密度分布函数，这样具有简单晶格结构的小离散速度集可以显着提高计算效率。我们将首次开发具有多种松弛时间格式的高阶LB模型，该模型不仅适用于流体动力流动，也适用于高度非平衡流动。这项研究的结果将在NSF方程之外的介孔LB建模能力方面取得根本性的进步，并为气体流动的实用模拟工具奠定坚实的基础，特别是在工业相关的微/纳米流体系统几何中。

The micro/nano-fluidic technology associated with Micro/Nano-Electro-Mechanical Systems and Micro-Total-Analysis Systems is set to revolutionise the chemical, pharmaceutical and food industries. Flow simulation is critical in the design of these miniaturised devices, but there is a major problem when predicting gas flow behaviour at micro/nano-scales. The thermodynamic quasi-equilibrium hypothesis, on which the Navier-Stokes-Fourier (NSF) equations depend, is violated when the mean free path of the gas molecules is comparable to the characteristic dimension of the devices. While standard continuum NSF equations become invalid, molecular dynamics methods for whole flow-field simulation are beyond current computational capabilities. We propose a mesoscopic lattice Boltzmann (LB) method to fill this gap between continuum and molecular approaches, aiming to produce quantitatively accurate results for non-equilibrium gas flows but at a fraction of the computational cost of molecular dynamics methods. In addition to developing high-order mesoscopic LB models for both isothermal and thermal non-equilibrium flows, we will propose multiple relaxation time schemes to address different relaxation rates for different order velocity moments (including momentum and energy). For thermal flow, instead of seeking large discrete velocity sets to retain up to 5th-order velocity terms in the Hermite expansion approximation to the equilibrium distribution function, an additional energy density distribution function will be introduced so that small discrete velocity sets with simple lattice structures can significantly improve computational efficiency. For the first time, we will develop high-order LB models with multiple relaxation time schemes that will be applicable not only to hydrodynamic flow but also highly non-equilibrium flows. The results of this research will deliver a fundamental advance in mesoscopic LB modelling capability beyond the NSF equations and lay down a firm basis for a practical simulation tool for gas flows especially in industrially-relevant micro/nano-fluidic system geometries.