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

非平衡气体流动格子玻尔兹曼模拟的新型多弛豫时间高阶模型

• 批准号: EP/F028865/1
• 负责人: Yonghao Zhang
• 金额: $ 31.91万
• 依托单位: University of Strathclyde
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2008
• 资助国家: 英国
• 起止时间: 2008 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FF028865%2F1
• 关键词: Novel; Multi; relaxation; time; order

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.

与微/纳米机电系统和微全分析系统相关的微/纳米流体技术将彻底改变化学、制药和食品行业。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尺寸相当时，纳维-斯托克斯-傅立叶 (NSF) 方程所依赖的热力学准平衡假说就会被违反。虽然标准连续 NSF 方程变得无效，但用于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）方法来填补连续介质方法和分子方法之间的差距，旨在为非平衡气流产生定量准确的结果，但计算成本仅为分子动力学方法的一小部分。除了开发用于等温和热非平衡流的高阶介观LB模型外，我们还将提出多种弛豫时间方案来解决不同阶速度矩（包括动量和能量）的不同弛豫率。对于热流，不是寻求大的离散速度集来在平衡分布函数的埃尔米特展开近似中保留高达五阶速度项，而是引入额外的能量密度分布函数，使得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弛豫时间方案的高阶 LB 模型，该模型不仅适用于流体动力流动，而且适用于高度非平衡流动。这项研究的结果将为介观LB建模能力带来超越NSF方程的根本性进步，并为气体流动的实用模拟工具（特别是在工业相关的微/纳米流体系统几何形状中）奠定坚实的基础。

项目成果

Accuracy analysis of high-order lattice Boltzmann models for rarefied gas flows

• DOI: 10.1016/j.jcp.2010.10.023
• 发表时间: 2009-08
• 期刊: J. Comput. Phys.
• 作者: J. Meng;Yonghao Zhang

Simulating fluid flows in micro and nano devices: the challenge of non-equilibrium behaviour

• DOI: 10.1166/jctn.2009.1263
• 发表时间: 2009-10
• 期刊: Journal of Computational and Theoretical Nanoscience
• 作者: J. Reese;Yonghao Zhang

Analytical Solution for the Lattice Boltzmann Model Beyond Naviers-Stokes

纳维-斯托克斯之外的格子玻尔兹曼模型的解析解

• DOI: 10.4208/aamm.10-10s09
• 发表时间: 2010
• 期刊: Advances in Applied Mathematics and Mechanics
• 影响因子: 1.4
• 作者: Zhang J