559 RWTH Publication No: 811901        2020       
TITLE Modeling, Control and Numerics of Gas Networks
AUTHORS Martin Gugat, Michael Herty
ABSTRACT In this article we survey recent progress on mathematical results on gas flow in pipe networks with a special focus on questions of control and stabilization. We briefly present the modeling of gas flow and coupling conditions for flow through vertices of a network. Our main focus is on gas models for spatially one-dimensional flow governed by hyperbolic balance laws. We survey results on classical solutions as well as weak solutions. We present results on well--posedness, controllability, feedback stabilization, the inclusion of uncertainty in the models and numerical methods.
KEYWORDS Hyperbolic Balance Laws, Stabilization, Exact Controllability, Modeling of Gas Flow, Finite-Volume Schemes, Optimal control, Uncertainty
DOI 10.1016/bs.hna.2021.12.002
PUBLICATION Handbook of Numerical Analysis, Volume 23, 2022, Pages 59-86