Well-balanced scheme for gas-flow in pipeline networks

Yogiraj Mantri; Michael Herty; Sebastian Noelle; Yogiraj Mantri; Michael Herty; Sebastian Noelle

doi:10.3934/nhm.2019026

Networks and Heterogeneous Media

2019, Volume 14, Issue 4: 659-676. doi: 10.3934/nhm.2019026

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Well-balanced scheme for gas-flow in pipeline networks

Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany

Received: 01 June 2018 Revised: 01 May 2019
Primary: 35L60, 35L65, 76M12

Gas flow through pipeline networks can be described using $ 2\times 2 $ hyperbolic balance laws along with coupling conditions at nodes. The numerical solution at steady state is highly sensitive to these coupling conditions and also to the balance between flux and source terms within the pipes. To avoid spurious oscillations for near equilibrium flows, it is essential to design well-balanced schemes. Recently Chertock, Herty & Özcan[11] introduced a well-balanced method for general $ 2\times 2 $ systems of balance laws. In this paper, we simplify and extend this approach to a network of pipes. We prove well-balancing for different coupling conditions and for compressors stations, and demonstrate the advantage of the scheme by numerical experiments.
- Well-balanced schemes,
- hyperbolic balance laws,
- flows in networks
Citation: Yogiraj Mantri, Michael Herty, Sebastian Noelle. Well-balanced scheme for gas-flow in pipeline networks[J]. Networks and Heterogeneous Media, 2019, 14(4): 659-676. doi: 10.3934/nhm.2019026

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Abstract

Gas flow through pipeline networks can be described using $ 2\times 2 $ hyperbolic balance laws along with coupling conditions at nodes. The numerical solution at steady state is highly sensitive to these coupling conditions and also to the balance between flux and source terms within the pipes. To avoid spurious oscillations for near equilibrium flows, it is essential to design well-balanced schemes. Recently Chertock, Herty & Özcan[11] introduced a well-balanced method for general $ 2\times 2 $ systems of balance laws. In this paper, we simplify and extend this approach to a network of pipes. We prove well-balancing for different coupling conditions and for compressors stations, and demonstrate the advantage of the scheme by numerical experiments.

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