Friedrich-Alexander-Universität Erlangen-Nürnberg
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Finite Time Blow-up of Traveling Wave Solutions for the Flow of Real Gas through Pipeline Networks
(2016)
In the context of gas transportation, analytical solutions are essential
for the understanding of the underlying dynamics described
by a system of partial differential equations. We derive traveling wave
solutions for the 1-d isothermal Euler equations. A non-constant compressibility
factor is used to describe the correlation between density
and pressure. The blow-up of the traveling wave solution in finite time
is proven. We then extend our analysis to networks under appropriate
coupling conditions and derive compatibility conditions to fulfill these
coupling conditions.