Geodesic
Calculation of transient fluid flow regimes in pipeline networks
Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 2, pp. 12-23.

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We consider the calculation problem of flow regimes of transient processes in oil pipeline networks of complicated loop-back structure. The fluid flow in each linear pipe is described by a system of two first-order linear hyperbolic partial differential equations. At the junctions of the network, there are fulfilled unseparated boundary conditions determined by the first Kirchhoff law and by the continuity of the flow. We propose a scheme for the numerical solution to the problem based on the application of the grid method and obtain formulas that are an analog of the sweep method and do not depend on the number of junctions, pipes, and the structure of the pipeline network. Numerical experiments applying the proposed approach are implemented, some analysis of the results is carried out.
Keywords: transient regime, pipeline network, system of hyperbolic equations, unseparated boundary conditions, grid method, sweep method. 
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K. R. Aida-zade; Y. R. Ashrafova. Calculation of transient fluid flow regimes in pipeline networks. Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 2, pp. 12-23. http://geodesic.mathdoc.fr/item/SJIM_2015_18_2_a1/

[1] Aida-zade K. R., “Vychislitelnye zadachi na gidravlicheskikh setyakh”, Zhurn. vychisl. matematiki i mat. fiziki, 29:2 (1989), 184–193 | MR | Zbl

[2] Seok Woo Hong, Kim Ch., “A new finite volume method on junction coupling and boundary treatment for flow network system analyses”, Internat. J. Numer. Methods Fluids, 65:6 (2011), 707–742 | DOI | MR | Zbl

[3] Akhmetzyanov A. V., Salnikov A. M., Spiridonov S. V., “Mnogosetochnye balansovye modeli nestatsionarnykh potokov v slozhnykh gazotransportnykh sistemakh”, Setevye modeli v upravlenii, Spets. vyp., Upravlenie bolshimi sistemami, 30.1, izd. IPU RAN, M., 2010, 230–251

[4] Aida-zade K. R., Asadova J. A., “Study of transients in oil pipelines”, Automat. Remote Control, 72:12 (2011), 2563–2577 | DOI | Zbl

[5] Aliev R. A., Belousov V. D., Nemudrov A. G. i dr., Truboprovodnoi transport nefti i gaza, Ucheb. dlya vuzov, Nedra, M., 1988

[6] Smirnov M. E., Verigin A. N., Nezamaev N. A., “Computation of unsteady regimes of pipeline systems”, Russian J. Appl. Chemistry, 83:3 (2010), 572–578 | DOI

[7] Kuzmin D., A Guide to Numerical Methods for Transport Equations, Friedrich-Alexander-Universitat, Erlangen–Nürnberg, 2010

[8] Aida-zade K. R., Ashrafova E. R., “Opredelenie mesta razryva i ob'ema utechki v magistralnom nefteprovode pri nestatsionarnom rezhime”, Trudy RGU nefti i gaza imeni I. M. Gubkina, 2012, no. 2/267, 78–84

[9] Aida-zade K. R., Ashrafova E. R., “Localization of the points of leakage in an oil main pipeline under non-stationary conditions”, J. Engrg Phys. Thermophys., 85:5 (2012), 1148–1156 | DOI | MR

[10] Charnyi I. A., Neustanovivsheesya dvizhenie realnoi zhidkosti v trubakh, Nedra, M., 1975

[11] Voevodin A. F., “Metod progonki dlya raznostnykh uravnenii, opredelennykh na komplekse”, Zhurn. vychisl. matematiki i mat. fiziki, 13:2 (1973), 494–497 | MR | Zbl

[12] Voevodin A. F., Shugrin S. M., Metody resheniya odnomernykh evolyutsionnykh sistem, Nauka, Novosibirsk, 1993 | MR

[13] Shugrin S. M., “O neodnorodnykh raznostnykh skhemakh”, Zhurn. vychisl. matematiki i mat. fiziki, 6:1 (1966), 184–185

[14] Aida-zade K. R., Ashrafova E. R., “K resheniyu sistem differentsialnykh uravnenii blochnoi struktury s nerazdelennymi kraevymi usloviyami”, Sib. zhurn. industr. matematiki, 17:4 (2014), 3–13

[15] Abdullaev V. M., “Reshenie differentsialnykh uravnenii s nerazdelennymi mnogotochechnymi i integralnymi usloviyami”, Sib. zhurn. industr. matematiki, 15:3 (2012), 3–15 | MR

[16] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1977

[17] Samarskii A. A., Nikolaev E. S., Metody resheniya setochnykh uravnenii, Nauka, M., 1978 | MR

[18] Kuliev S. Z., “Podkhod k opredeleniyu koeffitsienta gidravlicheskogo soprotivleniya uchastka truboprovoda pri neustanovivshemsya rezhime dvizheniya zhidkosti”, Sib. zhurn. industr. matematiki, 18:1 (2015), 84–94 | DOI

[19] Faizullin R. T., “O reshenii nelineinykh algebraicheskikh sistem gidravliki”, Sib. zhurn. industr. matematiki, 2:2 (1999), 176–184 | Zbl

[20] Rudyak V. Ya., “Nelokalnye opredelyayuschie sootnosheniya, gidrodinamicheskie fluktuatsii i klassicheskie modeli gidrodinamiki”, Sib. zhurn. industr. matematiki, 1:1 (1998), 164–173 | MR | Zbl

[21] Zhikhalkina N. F., Faizullin R. T., “Zadacha minimizatsii summarnykh zatrat po transportirovke nefteproduktov”, Sib. zhurn. industr. matematiki, 5:1 (2002), 63–73 | MR | Zbl