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Numerical Investigation of the Duration of the Effect Exerted by Initial Regimes on the Process of Liquid Motion in a Pipeline

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Journal of Engineering Physics and Thermophysics Aims and scope

By using numerical methods, the duration of the effect exerted by initial regimes on the running state of a nonstationary process of liquid motion in a linear part of a pipeline has been investigated depending on the values of various parameters of this process. The process is described by a system of two hyperbolic-type partial differential equations.

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References

  1. A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  2. A. N. Tikhonov, Theorems of singleness for the heat conduction equation, Mat. Sborn., 42, No. 2, 199–216 (1935).

    MATH  MathSciNet  Google Scholar 

  3. G. O. Vafodorova, Problems without initial conditions for one nonclassical equation, Differents. Uravneniya, 39, No. 2, 278–280 (2003).

    MathSciNet  Google Scholar 

  4. G. O. Vafodorova, Problems without initial conditions for degenerate parabolic equations, Differ. Equ., 36, No. 12, 1876–1878 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  5. A. E. Shishkov, Existence of growing at infinity generalized solutions of initial-boundary value problems for linear and quasilinear parabolic equations, Ukr. Mat. Zh., 37, No. 4, 473–481 (1985).

    MathSciNet  Google Scholar 

  6. M. Bokalo, Dynamical problems without initial conditions for elliptic-parabolic equations in spatial unbounded domains, Electron. Differ. Equ., No. 178, 1–24 (2010). http://ejde.math.txstate.edu or http://ejde.math.unt.edu Ftp ejde. math.txstate.edu

  7. E. I. Moiseev and G. O. Vafodorova, Problems without initial conditions for some differential equations, Differ. Equ., 38, No. 8, 1162–1165 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  8. Y. A. Ashrafova, A problem of optimal control of the processes with unknown initial conditions, in: Proc. IV Int. Conf. ″Problems of Cybernetics and Informatics,″ Baku, Azerbaijan, Vol. 4, 35–37 (2012).

  9. K. R. Aida-zade and E. R. Ashrafova, Optimal control problems without initial conditions, in: Proc. III Int. Conf. ″Optimization and Applications″ (OPTIMA-2012), 23–30 September 2012, Koshta-da-Kaparika, Portugal, pp. 21–24.

  10. K. R. Aida-zade and Y. R. Ashrafova, Optimal control for boundary-value problems without initial conditions, in: Proc. 2nd Int. Russian-Uzbek Symp. ″Mixed-Type Equations and Akin Problems of Analysis and Informatics,″ El′brus (2012), pp. 22–24.

  11. A. I. Lobanov, T. K. Starozhilova, and G. T. Guriya, Numerical investigation of structure formation in blood coagulation, Mat. Model., 9, No. 8, 83–95 (1997).

    MATH  Google Scholar 

  12. F. I. Ataullakhanov, G. T. Guria, V. I. Sarbash, and R. I. Volkova, Spatiotemporal dynamics of clotting and pattern formation in human blood, Biochim. Biophys. Acta, 1425, 453–468 (1998).

    Article  Google Scholar 

  13. I. A. Charnyi, Nonstationary Motion of a Real Liquid in Pipes [in Russian], Nedra, Moscow (1975).

    Google Scholar 

  14. X. C. Yu and Q. P. Li, Shutdown and restart transient flow characteristic study in offshore multiphase pipeline, J. Eng. Thermophys., 29, No. 2, 251–255 (2008).

    Google Scholar 

  15. K. R. Aida-zade and D. A. Asadova, Analysis of the regimes of controlling transient processes in pipelines, J. Eng. Phys. Thermophys., 85, No. 1, 131–140 (2012).

    Article  Google Scholar 

  16. K. R. Aida-zade and E. R. Ashrafova, Localization of the points of leakage in an oil main pipeline under nonstationary conditions, J. Eng. Phys. Thermophys., 85, No. 5, 1148–1156 (2012).

    Article  Google Scholar 

  17. I. V. Kudinov, V. A. Kudinov, and A. V. Eremin, Distribution of viscous liquid fl ow velocity in a pipeline on hydraulic shock, J. Eng. Phys. Thermophys., 86, No. 2, 410–417 (2013).

    Article  Google Scholar 

  18. A. N. Volobuev and A. P. Tolstonogov, Features of viscous-fluid flow in an elastic pipeline, J. Eng. Phys. Thermophys., 82, No. 4, 749–755.

  19. A. A. Samarskii and A. V. Gulin, Numerical Methods [in Russian], Nauka, Moscow (1989).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Control Systems, National Academy of Sciences of Azerbaijan, 9 B. Vakhabzade Str., Baku, AZ, 1141, Azerbaijan

    E. R. Ashrafova

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  1. E. R. Ashrafova
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Correspondence to E. R. Ashrafova.

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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 88, No. 5, pp. 1199–1207, September–October, 2015.

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Ashrafova, E.R. Numerical Investigation of the Duration of the Effect Exerted by Initial Regimes on the Process of Liquid Motion in a Pipeline. J Eng Phys Thermophy 88, 1239–1247 (2015). https://doi.org/10.1007/s10891-015-1305-4

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  • DOI: https://doi.org/10.1007/s10891-015-1305-4

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