<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

Transient Flow in Gas Networks: Traveling waves

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Transient Flow in Gas Networks: Traveling waves"}

In the context of gas transportation, analytical solutions are helpful for the understanding of the underlying dynamics governed by a system of partial...

Transient Flow in Gas Networks: Traveling waves

Published Online: Jun 29, 2018

Page range: 341 - 348

Received: Apr 25, 2017

Accepted: Dec 29, 2017

DOI: https://doi.org/10.2478/amcs-2018-0025

Keywords
traveling wave, isothermal Euler equations, compressibility factor, gas network, blow-up, optimal control

© 2018 Martin Gugat, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Transient Flow in Gas Networks: Traveling waves

Published Online: Jun 29, 2018

Page range: 341 - 348

Received: Apr 25, 2017

Accepted: Dec 29, 2017

DOI: https://doi.org/10.2478/amcs-2018-0025

Keywordstraveling wave, isothermal Euler equations, compressibility factor, gas network, blow-up, optimal control

© 2018 Martin Gugat, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
traveling wave, isothermal Euler equations, compressibility factor, gas network, blow-up, optimal control