Numerical method of pipeline hydraulics identification at turbulent flow of viscous liquids



Published Dec 31, 2019
Kh. M. Gamzaev


A mathematical model for the process of incompressible viscous liquid unsteady turbulent flow in a pipeline is proposed, based on the semi-empirical theory of Prandtl turbulence. As part of this model, the problem of identifying the pipeline hydraulics is formulated. It is assumed that slippage of the flow on the pipeline wall meets the condition of Navier law. This problem belongs to the class of inverse problems related to the restoration of the parabolic equations right parts’ dependence on time. Next, a difference analogue of the formulated problem is constructed, and a special representation associated with the solution of two linear difference problems of the second order is proposed to solve the obtained difference problem. The result is an explicit formula to determine the approximate value of the differential pressure along the length of the pipeline for each discrete value of the time variable. On the basis of the proposed computational algorithm, numerical experiments for model problems were carried out.


How to Cite

Gamzaev KM. Numerical method of pipeline hydraulics identification at turbulent flow of viscous liquids. PST [Internet]. 2019Dec.31 [cited 2020Jul.16];3(2):118-24. Available from:


Download data is not yet available.
Abstract 54 | PDF file Downloads 91



pipeline transport, turbulent conditions, hydraulics, semi-empirical theory of turbulence, non-local integral condition, inverse problem

[1] Basniev K. S., Dmitriev N. M., Rosenberg G. D. Oil and Gas Hydromechanics. Moscow, Izhevsk: Institute of computer studies, 2005. 544 p. (In Russ)
[2] Lurie M. V. Mathematical modeling of pipeline transportation of oil, petroleum products and gas. M: GubkIn Russ State University of Oil and Gas, 2012. 456 p. (In Russ)
[3] Loitsyansky L. G. Mechanics of liquid and gas. Moscow: Drofa, 2003. 840 p. (In Russ)
[4] Boundary slip in Newtonian liquids: a review of experimental studies / C. Neto [et al.]. Reports on Progress in Physics. 2005. Vol. 68. Issue 12. Р. 2859–2897.
[5] Lauga E., Brenner M. P., Stone H. A. Microfluidics: the no-slip boundary condition. In: Handbook of Experimental Fluid Dynamics. New York : Springer, 2006. p. 1,219–1,240.
[6] Gamzaev Kh. M. Numerical method of solving a nonlocal problem for pipeline transportation of viscous liquids. Bulletin of Tomsk State University. Series “Mathematics. Mechanics. Physics”. 2017. Vol. 9. No. 2. p. 5–12. (In Russ)
[7] Borzenko E. I., Dyakova O. A., Shrager G. R. Study of slippage in case of viscous liquid flow in a curved channel. Bulletin of Tomsk State University. Mathematics and Mechanics. 2014. No. 2. p. 35–44. (In Russ)
[8] Gamzaev Kh. M. On a numerical method for determining the hydraulics of the pipeline. Science & Technologies: Oil and Oil Products Pipeline Transportation. 2013. No. 2. p. 33–35. (In Russ)
[9] Prandtl L. The fluid mechanics. Moscow, Izhevsk: SIC “Regular and chaotic dynamics”, 2002. 576 p. (In Russ)
[10] Samarsky A. A., Vabischevich P. N. Numerical methods for solving inverse problems of mathematical physics. Moscow: LKI Publishing house, 2009. 480 p. (In Russ)
[11] Vabischevich P. N., Vasilyev V. I., Vasilyeva M. V. Computational identification of the right part of the parabolic equation. Journal of computational mathematics and mathematical physics. 2015. Vol. 55. No. 6. p. 1,020–1,027. (In Russ)
[12] Gamzaev K. M. Numerical solution of combined inverse problem for generalized burgers equation. Journal of Mathematical Sciences. 2017. Vol. 221. Nо. 6. Р. 833–839.
[13] Aida-zade K. R., Rahimov A. B. An approach to numerical solution of some inverse problems for parabolic equations. Inverse problems in Science and Engineering. 2014. Vol. 22. No. 1–2. P. 96–111.
Original Work