Steady State Blended Gas Flow on Networks: Existence and Uniqueness of Solutions

2024/11/06 by Alena Ulke, Ulke, Alena, Michael Schuster +3
Computer Science · Engineering · #34B45 #93C15 #Analysis of PDEs (math.AP) #Distributed and Parallel Computing Systems #FOS: Mathematics #Numerical Analysis (math.NA) #Smart Grid Security and Resilience

paper · pdf · doi:10.48550/arxiv.2411.03841

openalex publication_date 2024/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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