Steady state blended gas flow on networks: Existence and uniqueness of solutions

Ulke A, Schuster M, Göttlich S (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Networks and Heterogeneous Media American Institute of Mathematical Sciences (AIMS)

Book Volume: 20

Pages Range: 903-937

Journal Issue: 3

DOI: 10.3934/nhm.2025039

Abstract

We prove an existence result for the steady-state flow of gas mixtures in networks. The model is based on the physical principles of the isothermal Euler equations, coupling conditions for the flow and pressure, and the mixing of incoming flows at the nodes. The state equation is based on a convex combination of the ideal gas equations of state for natural gas and hydrogen. We analyze the mathematical properties of the model, allowing us to prove the existence of solutions for tree-shaped networks and networks with a cycle. Numerical examples illustrate the challenges involved, when extending our approach to general network topologies.

Authors with CRIS profile

Michael Schuster Sonderforschungsbereich/Transregio 154 Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken

Involved external institutions

Universität Mannheim DE Germany (DE)

How to cite

APA:

Ulke, A., Schuster, M., & Göttlich, S. (2025). Steady state blended gas flow on networks: Existence and uniqueness of solutions. Networks and Heterogeneous Media, 20(3), 903-937. https://doi.org/10.3934/nhm.2025039

MLA:

Ulke, Alena, Michael Schuster, and Simone Göttlich. "Steady state blended gas flow on networks: Existence and uniqueness of solutions." Networks and Heterogeneous Media 20.3 (2025): 903-937.

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