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中国科学院大学学报 ›› 2002, Vol. 19 ›› Issue (4): 422-427.DOI: 10.7523/j.issn.2095-6134.2002.4.014

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固体中冲击波及其一维一阶非线性演化方程数值模拟

郑海山1, 杨宝俊2, 刘财2, 冯晅2   

  1. 1. 中国科学院地质与地球物理研究所, 北京 100101;
    2. 吉林大学地球物理系, 长春 130026
  • 收稿日期:2001-12-31 修回日期:2002-03-22 发布日期:2002-07-18
  • 作者简介:郑海山, 男, 1977 年6 月生, 博士生

Shock Waves in Solid Medium and Numerical Solutions of its One-Dimensional and First-Order Nonlinear Evolution Equations

ZHENG Hai Shan1, YANG Bao Jun2, LIU Cai2, FENG Xuan2   

  1. 1. Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100101;
    2. The Geophysics department of Jilin University, Changchun 130026
  • Received:2001-12-31 Revised:2002-03-22 Published:2002-07-18

摘要:

定义固体中的冲击波为冲击波阵面及其后状态物理量发生急剧变化的狭窄区域。利用前人讨论结果进一步探讨了 4种边界输入形式下的冲击波形成距离计算式。分别采用具有二阶精度的显式MacCormack差分格式和MacCormackTVD格式对黏弹性、热弹性以及非均匀性非线性固体介质中一维一阶非线性演化方程进行数值模拟研究,探讨了这些复杂介质中冲击波的形成及演化的基本性质,并较成功地避免了非物理解的产生

关键词: 冲击波, 非线性演化方程, 数值模拟

Abstract:

A definition to shock waves in solid medium, namely, a clear description to its fundamental properties, was given in this paper.We regard the thin area of waves in solid medium with sharp changing of its physical character as shock waves.Four different kinds of initial conditions were given to study the properties of the distance of shock wave formed in solid medium.The effect of factors, such as amplitude, initial frequency, nonlinear coeff iciency, etc.on the distance of shock w aves w ere studied in some details.Numerical methods, the explict MacCormack and MacCormack TVD schemes with finite differences, were used to study shock waves in solid respectively, which avoid causing some unphysical solutions.

Key words: shock wave, nonlinear evolution equation, numerical method

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