Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks

Erscheinungsjahr 2026
ISBN: 978-3-032-34968-2
Verlag: Birkhäuser

Buch, Englisch, 519 Seiten, Format (B × H): 155 mm x 235 mm

Reihe: International Series of Numerical Mathematics

This open-access book provides an overview of the state-of-the-art of mathematical approaches for networks with physical transport, in particular gas networks. This is motivated by the transformation of energy systems towards carbon neutrality and leads to fundamental mathematical challenges. Natural and hydrogen gas networks play a central role in this context, since they require a mathematical understanding of specific network structures with hierarchical hybrid models involving algebraic, ordinary, and partial differential–algebraic equations of hyperbolic type. Moreover, considering such networks in a market environment, ensuring feasibility of all market contracts under uncertain data and technical constraints requires certified methods that still pose challenges for current research and practice. Central to this effort is the integration of integer and nonlinear optimization under uncertainty as well as the design of new paradigms to handle the discrete–continuous interplay inherent in gas transportation.

The book gives an overview of some of the research results that have been obtained within the German Collaborative Research Center CRC / TRR 154 funded by the German Science Foundation from 2014-2026. These methodological advances not only provide enabling technologies for the operation of gas networks and gas markets energy network certification but also contribute new mathematics with applications to other networked infrastructures such as power grids and water systems.

The target audience is formed by researchers in the field of applied mathematics who want to know more about modelling, simulation, and optimization for solving challenging network-based systems, as well as domain experts in gas networks who want to get insights into the underlying mathematical questions.

This book addresses United Nation’s Sustainable Development Goals 7 (Affordable and Clean Energy), 9 (Industry, Innovation and Infrastructure) and 13 (Climate Action).

Zielgruppe

Research

Autoren/Hrsg.

Martin, Alexander

Liers, Frauke

Hante, Falk

Lang, Jens

Pfetsch, Marc

Tischendorf, Caren

Ulbrich, Stefan

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik

Inhaltsverzeichnis

Preface.- Acknowledgements.- Part I Hierarchical Modeling for Simulation and Control of Gas Network Dynamics.- 1. Introduction to Hierarchical Modeling for Simulation and Control of Gas Network Dynamics by Jens Lang and Caren Tischendorf.- 2. A Catalog of Gas Network Models: PDEs, Coupling Conditions, and Numerical Schemes by Tobias Breiten, Pia Domschke, Jan Giesselmann, Benjamin Hiller, Attila Karsai, Jens Lang, Volker Mehrmann, Riccardo Morandin, Caren Tischendorf, and Tabea Tscherpel.- 3. Gas Mixtures on Networks: Modeling, Simulation and Optimization by Pascal Börner, Jan Giesselmann, Varun M. Kumar, Marc E. Pfetsch, Michael Thiele, and Tabea Tscherpel.- 4. Optimal Control Under Constrained Pressure Fluctuation by Martin Gugat, Henning Sauter, Michael Schuster, and Caren Tischendorf.- Part II Discrete-Continuous Optimization for Gas Networks.- 5. Introduction to Discrete-Continuous Optimization for Gas Networks by Alexander Martin and Marc E. Pfetsch.- 6. Mixed-Integer Nonlinear Optimization in the Context of Gas Networks by Robert Burlacu, Adrian Göß, Günter Leugering, Alexander Martin, Marc E. Pfetsch, Martin Schmidt, and Johannes Thürauf.- 7. Potential-Based Flows – An Overview by Marc E. Pfetsch, Martin Schmidt, Martin Skutella, and Johannes Thürauf.- 8. Models for Gas Markets byVeronika Grimm, Julia Grübel, Johannes Hahn, Max Klimm, Lars Schewe, Martin Schmidt, and Gregor Zöttl.- Part III Optimization under Uncertainty for Gas Networks.- 9. Introduction to Optimization under Uncertainty for Gas Networks by Frauke Liers and Stefan Ulbrich.- 10. From Probabilistic to Probust Constraints: Optimization Under Uncertainty by Daniela Bernhard, Caroline Geiersbach, Martin Gugat, Holger Heitsch, René Henrion, Jens Lang, Frauke Liers, Rüdiger Schultz, Michael Schuster, Michael Stingl, and Hendrik Wilka.- 11. Continuous Stochastic Gradient and Spherical Radial Decomposition by Daniela Bernhard, Holger Heitsch, René Henrion, Frauke Liers, Michael Stingl, Andrian Uihlein, and Viktor Zipf.- 12. Incremental–Decremental Optimization for the Transition to Hydrogen by Yann Disser, Max Klimm, Annette Lutz, and Lea Strubberg.- Part IV PDE-based Optimization and Control for Gas Network Applications.- 13. Introduction to PDE-based Optimization and Control for Gas Network Applications by Falk M. Hante and Stefan Ulbrich.- 14. Optimal Control of Discontinuous Solutions of Hyperbolic Systems of Balance Laws by Jannik Breitkopf and Stefan Ulbrich.- 15. Sequential Action Control for Hybrid Dynamical Models of Gas Networks by Yan Brodskyi, Falk M. Hante, and Antonia Topalovic.- 16. The Turnpike Property and the Optimal Control of Gas Networks by Martin Gugat and Michael Schuster.- 17. Domain Decomposition for Gas Network Control by Falk M. Hante, Martin Hernandez, Günter Leugering, Martin Schmidt, and Enrique Zuazua.- 18. A PDE-Constrained Generalized Nash Equilibrium Approach for Modeling Gas Transport with Strategic Suppliers by Veronika Grimm, Michael Hintermüller, Olivier Huber, Lars Schewe, Martin Schmidt, and Gregor Zöttl.- 19. -Wasserstein Distances on Networks and 3D to 1D Convergence by Martin Burger, Ariane Fazeny, Gilles Mordant, and Jan-Frederik Pietschmann.- Part V Introduction to Practical Challenges and a Benchmark Instance for Gas–Hydrogen Networks.- 20. Introduction to Practical Challenges and a Benchmark Instance for Gas–Hydrogen Networks by Frauke Liers and Alexander Martin.- 21. Gas2Hydro – A Combined Natural Gas–Hydrogen Instance by Daniela Bernhard, Julian Born, Yann Disser, Caroline Geiersbach, Johannes Hahn, Anton Hoof, and Lea Strubberg.- 22. Mathematical Questions Arising from Practical Challenges in Gas Networks byJulia Grübel, Frauke Liers, Alexander Martin, Lars Schewe, and Michael Schuster.

Über Autor(innen)

The editorial team consists of outstanding researchers with extensive expertise in modeling, simulation, and optimization. The have been engaged in the CRC / TRR 154 from its beginnings and are based in the three project sites Erlangen, Nürnberg, Darmstadt, and Berlin. They bring together extensive knowledge and perspectives on the topics covered by this book.