Steady State Blended Gas Flow on Networks: Existence and Uniqueness of Solutions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916470214098944 |
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| author | Ulke, Alena Schuster, Michael Göttlich, Simone |
| author_facet | Ulke, Alena Schuster, Michael Göttlich, Simone |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03841 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Steady State Blended Gas Flow on Networks: Existence and Uniqueness of Solutions Ulke, Alena Schuster, Michael Göttlich, Simone Analysis of PDEs Numerical Analysis 34B45, 93C15 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. |
| title | Steady State Blended Gas Flow on Networks: Existence and Uniqueness of Solutions |
| topic | Analysis of PDEs Numerical Analysis 34B45, 93C15 |
| url | https://arxiv.org/abs/2411.03841 |