格子玻尔兹曼正则化碰撞模型的理论进展

李旭晖; 单肖文; 段文洋

doi:10.7638/kqdlxxb-2020.0426

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格子玻尔兹曼正则化碰撞模型的理论进展

专栏——格子玻尔兹曼方法及应用 | 更新时间：2026-05-28

- 格子玻尔兹曼正则化碰撞模型的理论进展
- Theoretical progress on regularized lattice Boltzmann collision models
- 空气动力学学报 2022年40卷第3期页码：46-64
- 作者机构：
  
  1. 哈尔滨工程大学船舶工程学院,哈尔滨,150001
  2. 南方科技大学力学与航空航天工程系,深圳,518055
- 作者简介：
  
  李旭晖*（1987-），湖南衡阳人，副教授，研究方向：格子玻尔兹曼方法理论建模及其应用. E-mail：lixuhui@hrbeu.edu.cn
- 基金信息：
  
  哈尔滨工程大学中央高校基本业务费（3072021CFJ0101）;黑龙江省自然科学基金联合引导项目（LH2021A007）
- DOI：10.7638/kqdlxxb-2020.0426
  中图分类号： O352
- 纸质出版：2022
- 稿件说明：
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李旭晖, 单肖文, 段文洋. 格子玻尔兹曼正则化碰撞模型的理论进展[J]. 空气动力学学报, 2022, 40(3): 46−64.

LI Xuhui, SHAN Xiaowen, DUAN Wenyang. Theoretical progress on regularized lattice Boltzmann collision models[J]. 2022, 40(3): 46-64.
李旭晖, 单肖文, 段文洋. 格子玻尔兹曼正则化碰撞模型的理论进展[J]. 空气动力学学报, 2022, 40(3): 46−64. DOI： 10.7638/kqdlxxb-2020.0426

LI Xuhui, SHAN Xiaowen, DUAN Wenyang. Theoretical progress on regularized lattice Boltzmann collision models[J]. 2022, 40(3): 46-64. DOI： 10.7638/kqdlxxb-2020.0426.

摘要

数值稳定性问题一直是困扰格子玻尔兹曼方法在高雷诺数高马赫数流动中广泛应用的瓶颈。在格子玻尔兹曼方法领域改良碰撞模型的数值稳定性和精度一直是近30年来的研究难点和热点。正则化碰撞模型作为众多碰撞模型的一个重要分支，近几年来取得了重要理论进展，目前已在高雷诺数湍流模拟、高马赫数可压缩流动以及气动声学领域得到了广泛应用。本文系统地回顾了正则化碰撞模型的发展历史，并建立了一个系统的理论框架阐述不同正则化碰撞模型之间的理论联系。同时，揭示了正则化多松弛碰撞模型的理论本质，就是在与坐标无关且自相似的矩空间中将离散格子模型表达不了的高阶动理学矩进行快速松弛，以避免虚假模态对水动力学方程的影响。

Abstract

Numerical stability has always been the bottleneck that plagues the wide application of lattice Boltzmann methods in the scenario of high Reynolds number and high Mach number flows. It has been a research hotspot and difficulty in the past three decades to improve the numerical stability and accuracy of the collision models for lattice Boltzmann methods. As an important branch of many collision models

the regularized collision model has made massive theoretical progress in recent years

and has been widely applied in the fields of high Reynolds number turbulent flow

high Mach number compressible flow and aeroacoustics flow. The present study systematically reviews the development history of regularized collision models

and establishes a systematic theoretical framework to illustrate the underlying theoretical connection among different regularized collision models. Meanwhile

the present work reveals the theoretical essence of the regularized multi-relaxation collision model

which is to rapidly relax the higher-order kinetic moments that cannot be expressed by the discrete lattice model in a coordinate-independent and self-similar moment space

so as to avoid the spurious modes affecting the hydrodynamic equations.

关键词

Keywords

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