圆柱形汇聚激波诱导 Richtmyer-Meshkov不稳定的 SPH 模拟

徐建于; 黄生洪

doi:10.6052/0459-1879-19-041

圆柱形汇聚激波诱导 Richtmyer-Meshkov不稳定的 SPH 模拟

徐建于,
黄生洪^2), ,

中国科学技术大学工程科学学院,合肥 230026

基金项目: 1) 挑战专题TZ2016001; 国家自然科学基金(U1530125)资助项目.

详细信息

通讯作者:
2) 黄生洪,副教授,主要研究方向：先进SPH算法研究.E-mail: hshnpu@ustc.edu.cn

中图分类号: O34
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出版历程
- 收稿日期: 2019-01-31
- 刊出日期: 2019-07-17

NUMERICAL SIMULATION OF CYLINDRICAL CONVERGING SHOCK INDUCED RICHTMYER-MESHKOV INSTABILITY WITH SPH

Xu Jianyu,
Huang Shenghong^2), ,

School of Engineering Science, University of Science and Technology of China, Hefei 230026, China

摘要

摘要: 汇聚激波诱导不同物质界面的Richtmyer-Meshkov(RM)不稳定现象在惯性约束核聚变领域有重要的学术意义和工程背景.基于网格离散的宏观流体力学方法由于数值扩散问题往往需要高阶精度算法才能准确追踪界面演化,且对大变形和破碎合并等复杂界面追踪也极为困难.光滑粒子流体动力学(smoothed particlehydrodynamics,SPH)方法采用纯拉格朗日算法,可以有效克服上述难点.但经典SPH算法需采用人工黏性处理强间断,在激波间断处往往会出现严重的非物理振荡,对于涉及强冲击不稳定性问题,很难达到理想的模拟效果.本文采用基于HLL黎曼求解器的SPH算法,实现了对强激波和大密度比物质界面的有效分辨和追踪.一维数值校核证明了代码的可靠性、健壮性,并进一步模拟了二维圆柱形汇聚冲击波冲击四边形轻/重气界面诱导的RM不稳定性问题,与已有实验结果进行了对比,发现模拟结果与实验结果吻合.通过分析界面演化过程中的密度及压力变化,发现本文所采用的方法可准确地追踪激波与界面作用的复杂界面和波系演化规律.研究结果为进一步理解和解释汇聚冲击条件下的RM不稳定性机理奠定了基础.
- SPH /
- 黎曼求解器 /
- Richtmyer-Meshkov不稳定性 /
- 激波 /
- 圆柱形汇聚 /
- 数值模拟
Abstract: The Richtmyer-Meshkov (RM) instability induced by converging shock waves at interfaces of different substances has an important academic significance and engineering background in the field of inertial confinement fusion. The macroscopic fluid dynamics method based on grid discretization requires high order precision algorithm to track the interface evolution accurately because of numerical diffusion problem, and it is extremely difficult to track the complex interface evolution such as large deformation and fragmentation merging, etc. Smoothed particle hydrodynamics (SPH) method is a pure Lagrangian algorithm, which can effectively overcome the addressed difficulties. However, the classical SPH algorithm requires artificial viscosity to smooth the strong discontinuities, otherwise large non-physical oscillations may occur. For the problem involving strong shock instability, it is difficult to achieve ideal results. In this paper, the SPH algorithm based on HLL Riemann solver is adopted to effectively distinguish and track the strong shock wave and the material interface with a large density ratio. The reliability and robustness of the code were validated by four classical 1D shock tube tests, and it is found that the smoothing effect of the density algorithm used by SPH on the contact discontinuity can be improved by reducing the initial particle spacing. The smaller the initial particle spacing, the higher the numerical simulation accuracy, but it cannot be completely eliminated. However, the position of the interface is actually marked by the media properties of the particles, and does not affect the discrimination of the interface position under the SPH Lagrangian algorithm. Then the 2D cases of RM instability induced by cylindrical converging shock wave impacting at the quadrilateral light/heavy gas interface were simulated. It is found that the simulation results are quantitatively in good agreement with the existing experimental results. By analyzing the density and pressure changes in the process of interface evolution, it is also found that the models and methods adopted can accurately track the complex interfaces and shock waves evolution patterns during the RM instability process. The relevant results lay a foundation for further understanding and explanation of RM instability mechanism under extreme converging shock conditions.
- smoothed particle hydrodynamics /
- Riemann solver /
- Richtmyr-Meshkov instability /
- shock /
- cylindrical converging /
- numerical simulation

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