多层速度格子Boltzmann方法进展及展望

杨鲲; 单肖文

doi:10.7638/kqdlxxb-2021.0348

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多层速度格子Boltzmann方法进展及展望

专栏——格子玻尔兹曼方法及应用 | 更新时间：2026-05-28

- 多层速度格子Boltzmann方法进展及展望
- Progress and prospects of multi-speed lattice Boltzmann method
- 空气动力学学报 2022年40卷第3期页码：23-45
- 作者机构：
  
  1. 南方科技大学前沿与交叉科学研究院,深圳,518055
  2. 南方科技大学工学院力学与航空航天系,深圳,518055
- 作者简介：
  
  杨鲲（1987-），男，湖北人，副研究员，研究方向：湍流理论、格子波尔兹曼方法. E-mail：yangk@sustech.edu.cn
  单肖文*，研究员，研究方向：格子波尔兹曼方法，航空航天空气动力学. E-mail：shanxw@sustech.edu.cn
- 基金信息：
  
  国家科技重大专项（J2019-II-0006-0026，J2019-II-0013-0033）;国家自然科学基金（91752204）;广东省科学技术厅项目（2019B121203001，2020B121203000）;深圳市科技创新委员会项目（KQTD20180411143441009，JCYJ20180504165704491）
- DOI：10.7638/kqdlxxb-2021.0348
  中图分类号： O552.3
- 纸质出版：2022
- 稿件说明：
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杨鲲, 单肖文. 多层速度格子Boltzmann方法进展及展望[J]. 空气动力学学报, 2022, 40(3): 23−45.

YANG Kun, SHAN Xiaowen. Progress and prospects of multi-speed lattice Boltzmann method[J]. 2022, 40(3): 23-45.
杨鲲, 单肖文. 多层速度格子Boltzmann方法进展及展望[J]. 空气动力学学报, 2022, 40(3): 23−45. DOI： 10.7638/kqdlxxb-2021.0348

YANG Kun, SHAN Xiaowen. Progress and prospects of multi-speed lattice Boltzmann method[J]. 2022, 40(3): 23-45. DOI： 10.7638/kqdlxxb-2021.0348.

摘要

格子Boltzmann方法（LBM）自20世纪90年代问世以来，由于计算高效、实施简捷，在多种复杂流动的数值模拟中得到了广泛应用。传统以平衡态分布函数泰勒展开结合半经验理论推导出的LBM模型需要使用低马赫数假设，一度被认为只能适用于等温弱可压流动的计算。近年来将LBM拓展到可压缩和热流计算的模型日益增多，其中在每个离散速度方向有多个速度模态的多层速度模型，因只使用单一分布函数，物理描述上更接近事实而受到了广泛关注。我们简述了几类典型的多层速度模型的构造思路，包括早期的多层速度模型、Watari-Tsutahara模型、比热比可变多层速度模型和Hermite多项式模型。由于Hermite多项式展开法构造的多层速度模型在数学解释上较为自洽，且其低阶形态与传统等温弱可压LBM模型一致，我们着重梳理和归纳了Hermite多项式模型的构造原理与离散速度模型的求解过程，以及时间和空间离散方法。最后对LBM与传统计算流体力学方法的结合进行了简要介绍，例如LBM有限差分、LBM有限体积和LBM有限元方法，并对LBM多层速度模型目前存在的问题和未来发展方向进行了总结。

Abstract

Due to high computational efficiency and implementation simplicity

lattice Boltzmann method (LBM) has been widely used to simulate a variety of complex flows since its invention in the 1990s. Traditional LBM

derived from Taylor expansion of equilibrium distribution function and semi-empirical theory

employing a low Mach-number assumption

was once considered only capable for isothermal weakly compressible flows. In recent years

several models extending LBM to compressible and thermal flow have been proposed

among those the multi-speed model with multiple speed magnitude in each directions

has received widespread attention since its single distribution function is more physically realistic. We described the ideas of several typical multi-speed models

including multi-speed models of early ages

Watari-Tsutahara model

flexible specific-heat ratio and Hermite polynomial model. Since the multi-speed model constructed by Hermite polynomial expansion method is more mathematically self-consistent

and its low-order form is consistent with the traditional isothermal weakly compressible LBM model

we focus on interpretation of the multi-speed models constructed by Hermite polynomial expansion method

including the construction principle

procedure of discrete velocity model solution and time-space discrete method. Several combination of LBM and traditional computational fluid dynamics method

including finite difference LBM

finite volume LBM

and finite element LBM are briefed. The remained issues and future directions of LBM multi-speed models are summarized in the end.

关键词

Keywords

references

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