Skip to main content
SpringerLink
Log in

Numerical study of dynamic phase transitions in shock tube

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Shock tube problem of a van der Waals fluid with a relaxation model was investigated. In the limit of relaxation parameter tending towards zero, this model yields a specific Riemann solver. Relaxing and relaxed schemes were derived. For an incident shock in a fixed tube, numerical simulations show convergence toward the Riemann solution in one space dimension. Impact of parameters was studied theoretically and numerically. For certain initial shock profiles, nonclassical reflecting wave was observed. In two space dimensions, the effect of curved wave fronts was studied, and some interesting wave patterns were exposed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Baker G A. Quantitative theory of critical phenomena[M]. San Diego: Academic Press, 1990.

    Google Scholar 

  2. Hsieh Dinyu, Tang Shaoqiang, Wang Xiaoping. On hydrodynamic instabilities, chaos and phase transition[J]. Acta Mech Sinica, 1996, 12(1):1–14.

    Article  MATH  Google Scholar 

  3. Shu C W. A numerical method for systems of conservation laws of mixed type admitting hyperbolic flux splitting[J]. J Comp Phys, 1992, 21(100):424–429.

    Article  Google Scholar 

  4. Hsieh Dinyu, Wang Xiaoping. Phase transition in van der Waals fluid[J]. SIAM J Appl Math, 1997, 57(4):871–892.

    Article  MATH  MathSciNet  Google Scholar 

  5. Slemrod M. Admissibility criteria for propagating phase boundaries in a van der Waals fluid[J]. Arch Rat Mech Anal, 1983, 4(81):301–315.

    MathSciNet  Google Scholar 

  6. Jin Sin, Xin Zhouping. The relaxation schemes for systems of conservation laws in arbitrary space dimensions[J]. Comm Pure Appl Math, 1995, 48:235–278.

    Article  MATH  MathSciNet  Google Scholar 

  7. Natalini R, Tang Shaoqiang. Discrete kinetic models for dynamic phase transitions[J]. Comm Appl Nonlinear Anal, 2000, 7:1–32.

    MATH  MathSciNet  Google Scholar 

  8. Tang Shaoqiang, Wang Ping. Pattern formation in dynamic phase transitions[J]. Chin Phys Lett, 2004, 21:1566–1568.

    Article  MathSciNet  Google Scholar 

  9. Tang Shaoqiang, Zhao Huijiang. Stability of Suliciu model for phase transitions[J]. Comm Pure Appl Anal, 2004, 3(4):545–556.

    Article  MATH  MathSciNet  Google Scholar 

  10. Wang Ping, Tang Shaoqiang. Liquid-gas coexistence equilibrium in a relaxation model[J]. Appl Math Mech (English Edition), 2005, 26(6):767–773.

    Article  MATH  Google Scholar 

  11. Fornberg B, Witham G B. A numerical and theoretical study of certain nonlinear wave phenomena[J]. Philos Trans Roy Soc London Ser A, 1978, 289:373–404.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116024, P. R. China

    Wang Ping Doctor  (王平)

  2. LTCS, Department of Mechanics and Engineering Science, Peking University, Beijing, 100871, P. R. China

    Tang Shao-qiang  (唐少强)

Authors
  1. Wang Ping Doctor  (王平)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tang Shao-qiang  (唐少强)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wang Ping Doctor  (王平).

Additional information

Communicated by HUANG Yong-nian

Project supported by the Major State Basic Research Project “Nonlinear Science” of China (No. G2000077305) and the National Natural Science Foundation of China (Nos. 10002002 and 90407021)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, P., Tang, Sq. Numerical study of dynamic phase transitions in shock tube. Appl Math Mech 28, 921–929 (2007). https://doi.org/10.1007/s10483-007-0709-z

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-007-0709-z

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation