Stationary states in gas networks

Martin Gugat; Falk M. Hante; Markus Hirsch-Dick; Günter Leugering; Martin Gugat; Falk M. Hante; Markus Hirsch-Dick; Günter Leugering

doi:10.3934/nhm.2015.10.295

Networks and Heterogeneous Media

2015, Volume 10, Issue 2: 295-320. doi: 10.3934/nhm.2015.10.295

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Stationary states in gas networks

1.
Lehrstuhl Angewandte Mathematik 2, Cauerstr. 11, 91058 Erlangen, Department Mathematik, Friedrich-Alexander Universität Erlangen-Nürnberg (FAU)

Received: 01 September 2014 Revised: 01 December 2014
93C20, 93C15.

Pipeline networks for gas transportation often contain circles. For such networks it is more difficult to determine the stationary states than for networks without circles. We present a method that allows to compute the stationary states for subsonic pipe flow governed by the isothermal Euler equations for certain pipeline networks that contain circles. We also show that suitably chosen boundary data determine the stationary states uniquely. The construction is based upon novel explicit representations of the stationary states on single pipes for the cases with zero slope and with nonzero slope. In the case with zero slope, the state can be represented using the Lambert--W function.
- Network,
- isothermal Euler equations,
- stationary state,
- circles,
- cycles,
- gas transportation network
Citation: Martin Gugat, Falk M. Hante, Markus Hirsch-Dick, Günter Leugering. Stationary states in gas networks[J]. Networks and Heterogeneous Media, 2015, 10(2): 295-320. doi: 10.3934/nhm.2015.10.295

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Abstract

Pipeline networks for gas transportation often contain circles. For such networks it is more difficult to determine the stationary states than for networks without circles. We present a method that allows to compute the stationary states for subsonic pipe flow governed by the isothermal Euler equations for certain pipeline networks that contain circles. We also show that suitably chosen boundary data determine the stationary states uniquely. The construction is based upon novel explicit representations of the stationary states on single pipes for the cases with zero slope and with nonzero slope. In the case with zero slope, the state can be represented using the Lambert--W function.

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