Finite Time Blow-up of Traveling Wave Solutions for the Flow of Real Gas through Pipeline Networks
- 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.