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Godunov Method for Calculating Multicomponent Heterogeneous Medium Flows

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Journal of Engineering Physics and Thermophysics Aims and scope

The modified Godunov method intended for integrating the nondivergent systems that describe a multivelocity heterogeneous mixture flow is presented. The linearized Riemann solver has been used in solving the Riemann problems.

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References

  1. H. Stewart and B. Wendroff, Two-phase flow: Models and methods, J. Comput. Phys., 56, 363 (1984).

    Article  MATH  MathSciNet  Google Scholar 

  2. V. S. Surov, One-velocity model of a heterogeneous medium, Mat. Modelir., 13, No. 10, 27–42 (2001).

    MATH  MathSciNet  Google Scholar 

  3. M. Baer and J. Nunziato, A two-phase mixture theory for deflagration-to-detonation transition (DDT) in reactive granular materials, Int. J. Multiphase Flow, 12, 861–889 (1986).

    Article  MATH  Google Scholar 

  4. E. Romenski and E. F. Toro, Hyperbolicity and one-dimensional waves in compressible two-phase flow model, Shock Waves, 13, 473–487 (2004).

    Article  MATH  Google Scholar 

  5. S. Gavrilyuk and R. Saurel, Mathematical and numerical modeling of two-phase compressible flows with microinertia, J. Comput. Phys., 175, 326–360 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  6. J. M. Herard, A three-phase flow model, Mat. Comput. Model., 45, 732–755 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  7. V. F. Kuropatenko, A model of a multicomponent medium, Dokl. Ross. Akad. Nauk, 403, No. 6, 761–763 (2005).

    Google Scholar 

  8. A. Zein, M. Hantke, and G. Warnecke, Modeling phase transition for compressible two-phase flows applied to metastable liquids, J. Comput. Phys., 229, 2964–2998 (2010).

    Article  MATH  MathSciNet  Google Scholar 

  9. M. S. Chung, K. S. Chang, and S. J. Lee, Numerical solution of hyperbolic two-fluid two-phase flow model with nonreflecting boundary conditions, Int. J. Eng. Sci., 40, 789–803 (2002).

    Article  MATH  Google Scholar 

  10. G. S. Yeom and K. S. Chang, A modifi ed HLLC-type Riemann solver for the compressible six-equation two-fluid model, Comput. Fluids, 76, 86–104 (2013).

    Article  MathSciNet  Google Scholar 

  11. V. S. Surov, Hyperbolic model of a multivelocity heterogeneous medium, Inzh.-Fiz. Zh., 85, No. 3, 495–502 (2012).

    Google Scholar 

  12. S. K. Godunov, A. V. Zabrodin, M. Ya. Ivanov, et al., Numerical Solution of Multidimensional Problems of Gas Dynamics [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  13. V. S. Surov, A certain modification of the Godunov method for calculating one-velocity multicomponent mixture flows, Mat. Modelir., 10, No. 3, 29–38 (1998).

    Google Scholar 

  14. V. S. Surov, Disintegration of an arbitrary discontinuity in a one-velocity heterogeneous mixture of compressible media, Teplofiz. Vys. Temp., 36, No. 1, 157–161 (1998).

    Google Scholar 

  15. V. S. Surov, Toward the calculation of flows of a one-velocity multicomponent mixture by the modified S. K. Godunov method, Inzh.-Fiz. Zh., 84, No. 4, 777–784 (2011).

    Google Scholar 

  16. V. S. Surov, The Busemann flow for a one-velocity model of a heterogeneous medium, Inzh.-Fiz. Zh., 80, No. 4, 45–51 (2007).

    Google Scholar 

  17. V. S. Surov, The Riemann problem for the one-velocity model of a multicomponent mixture, Teplofiz. Vys. Temp., 47, No. 2, 283–291 (2009).

    Google Scholar 

  18. V. S. Surov, On a method of approximate solution of the Riemann problem for a one-velocity flow of a multicomponent mixture, Inzh.-Fiz. Zh., 83, No. 2, 351–356 (2010).

    Google Scholar 

  19. V. S. Surov, Modeling the High-Rate Interaction of Droplets (Jets) of a Liquid with Barriers by Means of Air Shock Waves, Candidate’s Dissertation (in Physics and Mathematics), Novosibirsk (1993).

  20. V. S. Surov, On equations of a one-velocity heterogeneous medium, Inzh.-Fiz. Zh., 82, No. 1, 75–84 (2009).

    Google Scholar 

  21. G. G. Wallis, One-Dimensional Two-Phase Flow [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  22. E. F. Toro, Riemann solvers with evolved initial condition, Int. J. Numer. Methods Fluids, 52, 433–453 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  23. V. S. Surov, The Riemann problem for the multivelocity model of a multicomponent medium, Inzh.-Fiz. Zh., 86, No. 4, 869–876 (2013).

    Google Scholar 

  24. V. S. Surov, Nodal method of characteristics for calculating flows of a multivelocity heterogeneous medium, Inzh.-Fiz. Zh., 86, No. 4, 869–876 (2013).

    Google Scholar 

  25. A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Questions of the Numerical Solution of Hyperbolic Systems of Equations [in Russian], 2nd enlarged and revised edn., FIZMATLIT, Moscow (2012).

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Correspondence to V. S. Surov.

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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 87, No. 2, pp. 367–375, March–April, 2014.

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Surov, V.S. Godunov Method for Calculating Multicomponent Heterogeneous Medium Flows. J Eng Phys Thermophy 87, 376–384 (2014). https://doi.org/10.1007/s10891-014-1022-4

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  • DOI: https://doi.org/10.1007/s10891-014-1022-4

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