Geodesic
Transient flow in gas networks: Traveling waves
International Journal of Applied Mathematics and Computer Science, Tome 28 (2018) no. 2, pp. 341-348.

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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.
Keywords: traveling wave, isothermal Euler equations, compressibility factor, gas network, blow-up, optimal control
Mots-clés : fala wędrująca, równania Eulera, współczynnik ściśliwości, sieć gazowa, sterowanie optymalne 
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Gugat, M.; Wintergerst, D. Transient flow in gas networks: Traveling waves. International Journal of Applied Mathematics and Computer Science, Tome 28 (2018) no. 2, pp. 341-348. http://geodesic.mathdoc.fr/item/IJAMCS_2018_28_2_a8/

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