Hierarchical Gas Model Coupling on Networks

• Main Author: Mindt, Pascal
• Format: Others
• Language: en
• Published: 2019
• Online Access: https://tuprints.ulb.tu-darmstadt.de/8710/1/Dissertation_PascalMindt.pdf; Mindt, Pascal <http://tuprints.ulb.tu-darmstadt.de/view/person/Mindt=3APascal=3A=3A.html> : Hierarchical Gas Model Coupling on Networks. Technische Universität, Darmstadt [Ph.D. Thesis], (2019)

In recent years the simulation of gas flow on networks attracts increasing interest. Since natural sources of energy, like wind and solar power, might lack of continuity, some demands in energy are compensated by gas. Therefore, accurate simulations for gas transport are essential. However, a highly detailed simulation suffers from great computational costs. Consequently, it becomes natural to use models with less physical detail in pipes with lower activity, while for pipes with greater dynamics, models with higher physical detail are used. In the analytical part of this work, we consider a network, with one single junction and a given model hierarchy. It appears the question how these models are coupled at the junction and which kind of coupling conditions have to be posed such that a resulting solution is unique and physically correct, as far as it even exists. In order to answer the above questions, we propose mass-, energy- and entropy- preserving coupling conditions at the junction. By introducing, a so called generalized Riemann problem at the junction, i.e., piecewise constant initial data, all models are connectible to each other through the coupling conditions. Afterwards, we show well-posedness of the generalized Riemann problem, i.e., there exists a unique physically correct solution. The well-posedness above creates a foundation for a more general setting, the so called Cauchy problem, in which initial data needs to be integrable with small total variation only. Here, well-posedness is shown as well. Based on these results, even existence of an optimal control can be proven. In the second part of this work, we like to give some numerical illustrations, built on our analytical results.