基于动理学模型的多尺度随机粒子方法

费飞; 张俊; 柳朝晖

doi:10.7638/kqdlxxb-2018.0164

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基于动理学模型的多尺度随机粒子方法

研究论文 | 更新时间：2026-05-28

- 基于动理学模型的多尺度随机粒子方法
- Multi-scale stochastic particle method based on kinetic models
- 空气动力学学报 2019年37卷第5期页码：731-739
- 作者机构：
  
  1. 华中科技大学航空航天学院,武汉,430074
  2. 北京航空航天大学航空科学与工程学院,北京,100191
  3. 华中科技大学能源与动力工程学院煤燃烧国家重点实验室,武汉,430074
- 作者简介：
  
  费飞(1984-), 男, 江苏扬州人, 讲师, 研究方向:稀薄气体动力学.E-mail:ffei@hust.edu.cn
- 基金信息：
  
  国家自然科学基金青年项目（51506063）;国家数值风洞项目（NNW2018-ZT3B07）
- DOI：10.7638/kqdlxxb-2018.0164
  中图分类号： V211.3
- 纸质出版：2019
- 稿件说明：
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费飞, 张俊, 柳朝晖. 基于动理学模型的多尺度随机粒子方法[J]. 空气动力学学报, 2019, 37(5): 731-739.

FEI Fei, ZHANG Jun, LIU Zhaohui. Multi-scale stochastic particle method based on kinetic models[J]. 2019, 37(5): 731-739.
费飞, 张俊, 柳朝晖. 基于动理学模型的多尺度随机粒子方法[J]. 空气动力学学报, 2019, 37(5): 731-739. DOI： 10.7638/kqdlxxb-2018.0164.

FEI Fei, ZHANG Jun, LIU Zhaohui. Multi-scale stochastic particle method based on kinetic models[J]. 2019, 37(5): 731-739. DOI： 10.7638/kqdlxxb-2018.0164.

摘要

传统随机粒子方法的时空离散步长受分子碰撞尺度（分子平均自由程和平均碰撞时间）的限制，当空间和时间离散尺度远大于碰撞特征尺度时，其输运系数的数值误差显著增加，因此如直接利用这类方法对跨流域流动精确求解，其计算效率往往是极低的（如DSMC方法，Fokker-Planck和BGK模型随机粒子方法）。通过对随机粒子方法输运系数离散误差的分析可知，这主要是因为传统算法将模拟分子的运动和碰撞解耦计算引起的。针对这一问题，本文介绍了适合于跨流域流动模拟的多尺度Fokker-Planck和BGK模型随机粒子方法。通过分子运动求解中耦合碰撞作用，在连续流区域，改进的随机粒子方法在较大的时间步长下仍能够满足宏观流体力学方程的输运性质。理论和计算结果显示，多尺度Fokker-Planck和BGK模型随机粒子方法可以高效准确地模拟从稀薄流到连续流的跨流域气体流动。

Abstract

The spatial and temporal discretization of traditional stochastic particle methods are limited by the inherent collision scales (such as the molecular mean free path and mean collision time). When they are larger than the collision scales

the numerical error of the transport coefficients is significant. Therefore

the computational efficiency is extremely low in the multi-scale flow simulation using traditional stochastic particle methods

such as the DSMC method and stochastic particle methods based on the Fokker-Planck/BGK models. It is noted that their transport coefficients depend on the ratio of time step and mean collision time. This dependence is caused by the decoupling of molecule motion and collision. To overcome these problems

the multi-scale stochastic particle methods based on the Fokker-Planck and BGK model are developed. They can eliminate the restriction of the inherent collision scales by coupling collision in molecule motion. These improved particle schemes can ensure the accuracy of the transport properties in the whole flow regimes independent of the spatial-temporal discretization

and compute the gas flows from rarefied to continuum regimes efficiently and accurately.

关键词

Keywords

references

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