松弛模型中的液气共存平衡态

王平; 唐少强

松弛模型中的液气共存平衡态

王平¹,
唐少强²

1.
大连理工大学工程力学系工业装备结构分析国家重点实验室,大连 116024;
北京大学力学与工程科学系湍流国家重点实验室,北京 100871

基金项目: 国家重点基础研究专项基金资助项目"非线性科学"(G2000077305);国家自然科学基金资助项目(10002002;90407021)

详细信息

作者简介:
王平(1976- ),男,吉林辉南人,讲师,博士(联系人.Tel:+86-411-84707608;E-mail:wangp@dlut.edu.cn);唐少强(Tel/Fax:+86-10-62755410;E-mail:maotang@pku.edu.cn).

中图分类号: O359.1
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出版历程
- 收稿日期: 2003-07-08
- 修回日期: 2004-11-30
- 刊出日期: 2005-06-15

Liquid-Gas Coexistence Equilibrium in a Relaxation Model

WANG Ping¹,
TANG Shao-qiang²

1.
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, P. R. China;
LTCS, Department of Mechanics and Engineering Science, Peking University, Beijing 100871, P. R. China

摘要

摘要: 对密闭的一维有限长管道里的等温相变，研究了松弛模型中液气共存平衡态的稳定性．使用匹配渐近展开形式上推出了一阶扰动满足的线性系统．理论分析发现，初始小扰动通常会被耗散掉，然而在一些特殊情况下，它们会维持在一定的水平上．数值计算也表明了松弛机制对相变演化具有稳定作用．
- 相变 /
- 松弛 /
- 匹配渐近展开
Abstract: Stability of liquid-gas coexistence equilibrium in a relaxation model for isothermal phase transition in a sealed one-dimensional tube was discussed.With matched asymptotic expansion,a linear system for first order perturbations was derived formally.By solving this system analytically,it is shown that small initial perturbations are damped out in general;yet they may maintain at certain level for special cases.Numerical evidence is presented.This manifests the regularization effects of relaxation.
- phase transition /
- relaxation /
- matched asymptotic expansion

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参考文献(12)

[1]	HSIEH Din-yu,WANG Xiao-ping. Phase transition in Van der Waals fluid[J].SIAM Journal on Applied Mathematics,1997,57(4):871—892. doi: 10.1137/S0036139995295165
[2]	Slemrod M. Dynamic phase transitions in a Van der Waals fluid[J].Differential Equations,1984,52:1—23. doi: 10.1016/0022-0396(84)90130-X
[3]	Zumbrun K. Dynamical[KG3/4]. stability[KG3/4]. of[KG3/4]. phase[KG3/4]. transitions in the p-system with viscosity-capillarity[J].SIAM Journal on Applied Mathematics,2000,60(6):1913—1924.
[4]	Fife P, WANG Xiao-ping. Periodic structures in a Van der Waals system[J].Pro Roy Soc Edinburgh Sect A,1998,128:235—250. doi: 10.1017/S0308210500012762
[5]	HE Chang-hong，WANG Xiao-ping.Symmetric solutions for a two dimensional Van der Waals system[D].Mphil Thesis. Math Dept HKUST, 1998.
[6]	FAN Hai-tao.Traveling waves, Riemann problems and computations of the dynamics of liquid/vapor phase transitions[J].Differential Equations,1998,150:385—437. doi: 10.1006/jdeq.1998.3491
[7]	CHEN Xin-fu，WANG Xiao-ping.Phase transition near a liquid-gas coexistence equilibrium[J].SIAM Journal on Applied Mathematics，2000，61(2):454—471. doi: 10.1137/S0036139999354285
[8]	JIN Sin, XING Zhou-ping.The relaxation schemes for systems of conservation laws in arbitrary space dimensions[J].Communications on Pure and Applied Mathematics,1995,48(3):1—43.
[9]	Natalini R,TANG Shao-qiang.Discrete kinetic models for dynamical phase transitions[J].Communications on Pure and Applied Analysis,2000,7(2):1—32.
[10]	TANG Shao-qiang,ZHAO Hui-jiang.Stability of suliciu model for phase transitions[J].Communications on Pure and Applied Analysis,2004,3(4):545—556. doi: 10.3934/cpaa.2004.3.545
[11]	TANG Shao-qiang.Patterns in 2-D dynamic phase transitions[A].In:CHIEN Wei-zang Ed.Proceedings of the 4th International Conference on Nonlinear Mechanics[C].Shanghai:Shanghai University Press, 2002, 820—823.
[12]	HSIEH Ding-yu,TANG Shao-qiang,WANG Xiao-ping.On hydrodynamic instabilities, chaos and phase transition[J].Acta Mechanica Sinica,1996，12(1):1—14. doi: 10.1007/BF02486757

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松弛模型中的液气共存平衡态

作者简介:
王平(1976- ),男,吉林辉南人,讲师,博士(联系人.Tel:+86-411-84707608;E-mail:wangp@dlut.edu.cn);唐少强(Tel/Fax:+86-10-62755410;E-mail:maotang@pku.edu.cn).

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Liquid-Gas Coexistence Equilibrium in a Relaxation Model

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留言板

松弛模型中的液气共存平衡态

作者简介: 王平(1976- ),男,吉林辉南人,讲师,博士(联系人.Tel:+86-411-84707608;E-mail:wangp@dlut.edu.cn);唐少强(Tel/Fax:+86-10-62755410;E-mail:maotang@pku.edu.cn).

计量

出版历程

Liquid-Gas Coexistence Equilibrium in a Relaxation Model

计量

出版历程

目录

作者简介:
王平(1976- ),男,吉林辉南人,讲师,博士(联系人.Tel:+86-411-84707608;E-mail:wangp@dlut.edu.cn);唐少强(Tel/Fax:+86-10-62755410;E-mail:maotang@pku.edu.cn).