New coupling conditions for isentropic flow on networks

Yannick Holle; Michael Herty; Michael Westdickenberg; Yannick Holle; Michael Herty; Michael Westdickenberg

doi:10.3934/nhm.2020016

Networks and Heterogeneous Media

2020, Volume 15, Issue 4: 605-631. doi: 10.3934/nhm.2020016

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New coupling conditions for isentropic flow on networks

1.
Institut für Mathematik, RWTH Aachen University, Templergraben 55, 52062 Aachen, Germany
2.
Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Templergraben 55, 52062 Aachen, Germany

Received: 01 April 2020 Published: 12 July 2020
35L65, 76N15, 82C40

We introduce new coupling conditions for isentropic flow on networks based on an artificial density at the junction. The new coupling conditions can be derived from a kinetic model by imposing a condition on energy dissipation. Existence and uniqueness of solutions to the generalized Riemann and Cauchy problem are proven. The result for the generalized Riemann problem is globally in state space. Furthermore, non-increasing energy at the junction and a maximum principle are proven. A numerical example is given in which the new conditions are the only known conditions leading to the physically correct wave types. The approach generalizes to full gas dynamics.
- Hyperbolic conservation laws,
- networks,
- coupling condition,
- isentropic gas dynamics,
- kinetic model,
- maximum entropy dissipation
Citation: Yannick Holle, Michael Herty, Michael Westdickenberg. New coupling conditions for isentropic flow on networks[J]. Networks and Heterogeneous Media, 2020, 15(4): 605-631. doi: 10.3934/nhm.2020016

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Abstract

We introduce new coupling conditions for isentropic flow on networks based on an artificial density at the junction. The new coupling conditions can be derived from a kinetic model by imposing a condition on energy dissipation. Existence and uniqueness of solutions to the generalized Riemann and Cauchy problem are proven. The result for the generalized Riemann problem is globally in state space. Furthermore, non-increasing energy at the junction and a maximum principle are proven. A numerical example is given in which the new conditions are the only known conditions leading to the physically correct wave types. The approach generalizes to full gas dynamics.

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