Creator:

Gugat, Martin ; Wintergerst, David

Contributor:

Puig, Vicenç - ed. ; Sauter, Dominique - ed. ; Aubrun, Christophe - ed. ; Schulte, Horst - ed.

Title:

Transient flow in gas networks: Traveling waves

Subtitle:

.

Group publication title:

AMCS, volume 28 (2018)

Subject and Keywords:

traveling wave ; isothermal Euler equations ; compressibility factor ; gas networks ; blow-up ; optimal control

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.

Publisher:

Zielona Góra: Uniwersytet Zielonogórski

Date:

2018

Resource Type:

artykuł

DOI:

10.2478/amcs-2018-0025

Pages:

341-348

Source:

AMCS, volume 28, number 2 (2018) ; click here to follow the link

Language:

eng

License CC BY 4.0:

click here to follow the link

Rights:

Biblioteka Uniwersytetu Zielonogórskiego