Transient flow in gas networks: Traveling waves

• Autorzy: Gugat M. , Wintergerst D.

Identyfikatory

DOI

10.2478/amcs-2018-0025

• Języki publikacji: EN

Abstrakty

EN

In the context of gas transportation, analytical solutions are helpful for the understanding of the underlying dynamics governed by a system of partial differential equations. We derive traveling wave solutions for the one-dimensional isothermal Euler equations, where an affine linear compressibility factor is used to describe the correlation between density and pressure. We show that, for this compressibility factor model, traveling wave solutions blow up in finite time. We then extend our analysis to networks under appropriate coupling conditions and derive compatibility conditions for the network nodes such that the traveling waves can travel through the nodes. Our result allows us to obtain an explicit solution for a certain optimal boundary control problem for the pipeline flow.

Słowa kluczowe

EN

traveling wave; isothermal Euler equations; compressibility factor; gas network; blow-up; optimal control

PL

fala wędrująca; równania Eulera; współczynnik ściśliwości; sieć gazowa; sterowanie optymalne

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2018
• Tom: Vol. 28, no. 2
• Strony: 341--348
• Opis fizyczny: Bibliogr. 19 poz., rys., wykr.

Twórcy

autor

Gugat M.

• Department of Mathematics, Friedrich-Alexander University Erlangen–Nürnberg (FAU), Cauerstr. 11, 91058 Erlangen, Germany

autor

Wintergerst D.

• Department of Mathematics, Friedrich-Alexander University Erlangen–Nürnberg (FAU), Cauerstr. 11, 91058 Erlangen, Germany

Bibliografia

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• [7] Gugat, M., Hante, F., Hirsch-Dick, M. and Leugering, G. (2015). Stationary states in gas networks, Networks and Heterogeneous Media 10(2): 295–320.
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• [9] Gugat, M. and Ulbrich, S. (2017). The isothermal Euler equations for ideal gas with source term: Product solutions, flow reversal and no blow up, Journal of Mathematical Analysis and Applications 454(1): 439–452.
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• [13] Liu, M., Zang, S. and Zhou, D. (2005). Fast leak detection and location of gas pipelines based on an adaptive particle filter, International Journal of Applied Mathematics and Computer Science 15(4): 541–550.
• [14] Mugnolo, D. and Rault, J.-F. (2014). Construction of exact travelling waves for the Benjamin–Bona–Mahony equation on networks, Bulletin of the Belgian Mathematical Society Simon Stevin 21(3): 415–436.
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• [16] Osiadacz, A. (1987). Simulation and Analysis of Gas Networks, Gulf Publishing Company, Houston, TX.
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• [19] Whitham, G.B. (1974). Linear and Nonlinear Waves, Wiley, New York, NY.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).