Richtmyer-Meshkov不稳定性的格子Boltzmann数值模拟

冯永昌; 李会雄; 王太

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Richtmyer-Meshkov不稳定性的格子Boltzmann数值模拟

更新时间：2025-07-09

- Richtmyer-Meshkov不稳定性的格子Boltzmann数值模拟
- Numerical Simulation of Richtmyer-Meshkov Instability Using Lattice Boltzmann Method
- 西安交通大学学报 2012年46卷第11期页码：44-48
- 作者机构：
  
  西安交通大学动力工程多相流国家重点实验室,西安,710049
- 作者简介：
- 基金信息：
  
  : 2012-03-11. 作者简介: 冯永昌(1986-),男,博士生;李会雄(通信作者),男,教授,博士生导师. 基金项目: 国家自然科学基金资助项目(51111120092)
- DOI：
  中图分类号： O354.5
- 网络首发：2012-11-10，
  
  纸质出版：2012
- 稿件说明：
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冯永昌, 李会雄, 王太. Richtmyer-Meshkov不稳定性的格子Boltzmann数值模拟[J]. 西安交通大学学报, 2012,46(11):44-48.

Numerical Simulation of Richtmyer-Meshkov Instability Using Lattice Boltzmann Method[J]. 2012, 46(11): 44-48.
冯永昌, 李会雄, 王太. Richtmyer-Meshkov不稳定性的格子Boltzmann数值模拟[J]. 西安交通大学学报, 2012,46(11):44-48. DOI：

Numerical Simulation of Richtmyer-Meshkov Instability Using Lattice Boltzmann Method[J]. 2012, 46(11): 44-48. DOI：

摘要

为了探寻研究Richtmyer-Meshkov(RM)不稳定性的新方法

采用耦合双分布函数格子Boltzmann方法(LBM)

对激波作用下两种不同密度流体交界面的演化过程进行了数值模拟研究

着重讨论了RM不稳定性的行程和演化特征

给出了交界面的扰动增长率的变化规律

同时还研究了激波强度对扰动振幅的影响.结果表明:由于受RM不稳定性的影响

两种不同密度流体的交界面上

重流体演化成尖顶结构

而轻流体演化成气泡结构

最终由于斜压效应重流体的尖顶转变成蘑菇头形状; 交界面扰动增长率与Zhang-Sohn模型较吻合; 激波强度越大

扰动振幅增长率越高.研究表明所提的方法可以用于RM不稳定性的研究

有望成为两相流研究的新途径.

Abstract

To seek a new method to study the Richtmyer-Meshkov(RM)instability

a numerical study was performed for the evolution of the interface between two layers of fluid with different densities using the coupled double distribution function lattice-Boltzmann method(LBM). The research focused on the RM instability and the perturbation growth rates of the interface were presented. The influence of the Mach number upon the perturbation growth rate was explored. The results show that due to the RM instability

the heavy fluid falls to generate a spike and the light fluid rises to form a bubble

and at last the head of the spike changes to mushroom shape. The numerical perturbation growth rate is in agreement with the result by the Zhang-Sohn model. The perturbation growth rises with an increase in the Mach number of shock wave. It can be concluded that the present method is an efficient approach to the simulation for the RM instability and two-phase flow.

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Keywords

references

RICHTMYER R D. Taylor instability in shock acceleration of compressible fluids[J]. Communications on Pure Applied Mathematics, 1960, 13(2): 297-319.

MESHKOV E E. Instability of the interface of two gases accelerated by a shock wave[J]. Fluid Dynamics, 1969, 4(5): 101-104.

VETTER M, STURTEVANT B. Experiments on the Richtmyer-Meshkov instability of an air/SF6 interface[J]. Shock Waves, 1995, 4(5): 247-252.

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CHEN Feng, XU Aiguo, ZHANG Guangcai, et al. Highly efficient lattice Boltzmann model for compressible fluids: two-dimensional case[J]. Communications in Theoretical Physics, 2009, 52(4): 681-693.

LI Qing, HE Yaling, WANG Yong, et al. Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations[J]. Physical Review:E, 2007, 76(6): 056705.

PUPPO G, PIERACCINI S. Implicit-explicit schemes for BGK kinetic equations[J]. Journal of Scientific Computing, 2007, 32(1): 1-28.

GUO Zhaoli, ZHENG Chuguang, SHI Baochang. Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method[J]. Chinese Physics, 2002, 11(4): 366-374.

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ZHANG Q, SOHN S I. Nonlinear theory of unstable fluid mixing driven by shock wave[J]. Physics of Fluids, 1997, 9(4): 1106-1124.

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