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Number 2 - June 2018
Volume 28 - 2018
Transient flow in gas networks: Traveling waves
Martin Gugat, David Wintergerst
Abstract
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