Geodesic
Unsteady flows in deformable pipes: the energy conservation law
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems and methods in mechanics, Tome 300 (2018), pp. 76-85.

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We derive a quasi-one-dimensional energy equation that corresponds to the flow of a compressible viscous fluid in a deformable pipeline. To describe the flow of such a fluid in a pipeline, we couple this equation with the previously derived continuity and momentum equations as well as with the equations of state for the internal energies of the fluid, the pipe deformations, pressure, and the cross-sectional area of the pipe. The derivation of the equations is based on averaging over the pipeline cross section. The equations obtained are designed for numerical simulations of long-distance transportation of a compressible fluid. 
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     title = {Unsteady flows in deformable pipes: the energy conservation law},
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A. T. Il'ichev; S. I. Sumskoi; V. A. Shargatov. Unsteady flows in deformable pipes: the energy conservation law. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems and methods in mechanics, Tome 300 (2018), pp. 76-85. http://geodesic.mathdoc.fr/item/TM_2018_300_a4/

[1] A. V. Efimov, B. P. Demidovich (eds.), A Collection of Problems on Mathematics for Technical Universities, Part. 2: Special Sections of Mathematical Analysis, 2nd ed., Nauka, Moscow, 1986 (in Russian)

[2] Bourdarias C., Gerbi S., “A conservative model for unsteady flows in deformable closed pipes and its implicit second-order finite volume discretisation”, Comput. Fluids, 37:10 (2008), 1225–1237 | DOI | MR

[3] A. T. Il'ichev, “Stability of solitary waves in membrane tubes: A weakly nonlinear analysis”, Theor. Math. Phys., 193 (2017), 1593–1601 | DOI | DOI | MR

[4] L. I. Sedov, Mechanics of Continuous Media, v. 1, World Sci., River Edge, NJ, 1997 | MR | MR

[5] Streeter V. L., Wylie E. B., Bedford K. W., Fluid mechanics, WCB/McGraw-Hill, Boston, 1998

[6] Sumskoi S. I., Sofin A. S., Lisanov M. V., “Developing the model of non-stationary processes of motion and discharge of single- and two-phase medium at emergency releases from pipelines”, J. Phys.: Conf. Ser., 751 (2016), 012025 | DOI

[7] Sumskoi S. I., Sverchkov A. M., “Modeling of non-equilibrium processes in oil trunk pipeline using Godunov type method”, Phys. Procedia, 72 (2015), 347–350 | DOI

[8] Sumskoi S. I., Sverchkov A. M., Lisanov M. V., Egorov A. F., “Modelling of non-equilibrium flow in the branched pipeline systems”, J. Phys.: Conf. Ser., 751 (2016), 012022 | DOI

[9] Sumskoi S. I., Sverchkov A. M., Lisanov M. V., Egorov A. F., “Simulation of systems for shock wave/compression waves damping in technological plants”, J. Phys.: Conf. Ser., 751 (2016), 012023 | DOI

[10] Sumskoi S. I., Sverchkov A. M., Lisanov M. V., Egorov A. F., “Simulation of compression waves/shock waves propagation in the branched pipeline systems with multi-valve operations”, J. Phys.: Conf. Ser., 751 (2016), 012024 | DOI