A Central Scheme for Two Coupled Hyperbolic Systems

doi:10.1007/s42967-023-00306-5

Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (4): 2093-2118.doi: 10.1007/s42967-023-00306-5

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A Central Scheme for Two Coupled Hyperbolic Systems

Michael Herty, Niklas Kolbe, Siegfried Müller

Institute of Geometry and Applied Mathematics, RWTH Aachen University, Templergraben 55, Aachen 52062, Germany

收稿日期:2023-04-26 修回日期:2023-07-29 接受日期:2023-08-15 发布日期:2024-12-20
通讯作者: Niklas Kolbe,E-mail:kolbe@igpm.rwth-aachen.de;Michael Herty,E-mail:herty@igpm.rwth-aachen.de;Siegfried Müller,E-mail:mueller@igpm.rwth-aachen.de E-mail:kolbe@igpm.rwth-aachen.de;herty@igpm.rwth-aachen.de;mueller@igpm.rwth-aachen.de
基金资助:
Open Access funding enabled and organized by Projekt DEAL.The authors thank the Deutsche Forschungsgemeinschaft (DFG,German Research Foundation) for the financial support through 320021702/GRK2326,333849990/IRTG-2379,B04,B05,and B06 of 442047500/SFB1481,HE5386/18-1,19-2,22-1,23-1,25-1,ERS SFDdM035 and under Germany’s Excellence Strategy EXC-2023 Internet of Production 390621612 and under the Excellence Strategy of the Federal Government and the Länder.Support through the EU DATAHYKING is also acknowledged.

A Central Scheme for Two Coupled Hyperbolic Systems

Michael Herty, Niklas Kolbe, Siegfried Müller

Institute of Geometry and Applied Mathematics, RWTH Aachen University, Templergraben 55, Aachen 52062, Germany

Received:2023-04-26 Revised:2023-07-29 Accepted:2023-08-15 Published:2024-12-20
Contact: Niklas Kolbe,E-mail:kolbe@igpm.rwth-aachen.de;Michael Herty,E-mail:herty@igpm.rwth-aachen.de;Siegfried Müller,E-mail:mueller@igpm.rwth-aachen.de E-mail:kolbe@igpm.rwth-aachen.de;herty@igpm.rwth-aachen.de;mueller@igpm.rwth-aachen.de

摘要/Abstract

摘要： A novel numerical scheme to solve two coupled systems of conservation laws is introduced. The scheme is derived based on a relaxation approach and does not require information on the Lax curves of the coupled systems, which simplifies the computation of suitable coupling data. The coupling condition for the underlying relaxation system plays a crucial role as it determines the behaviour of the scheme in the zero relaxation limit. The role of this condition is discussed, a consistency concept with respect to the original problem is introduced, the well-posedness is analyzed and explicit, nodal Riemann solvers are provided. Based on a case study considering the p-system of gas dynamics, a strategy for the design of the relaxation coupling condition within the new scheme is provided.

关键词: Coupled conservation laws, Hyperbolic systems, Finite-volume schemes, Coupling conditions, Relaxation system

Abstract: A novel numerical scheme to solve two coupled systems of conservation laws is introduced. The scheme is derived based on a relaxation approach and does not require information on the Lax curves of the coupled systems, which simplifies the computation of suitable coupling data. The coupling condition for the underlying relaxation system plays a crucial role as it determines the behaviour of the scheme in the zero relaxation limit. The role of this condition is discussed, a consistency concept with respect to the original problem is introduced, the well-posedness is analyzed and explicit, nodal Riemann solvers are provided. Based on a case study considering the p-system of gas dynamics, a strategy for the design of the relaxation coupling condition within the new scheme is provided.

Key words: Coupled conservation laws, Hyperbolic systems, Finite-volume schemes, Coupling conditions, Relaxation system

Michael Herty, Niklas Kolbe, Siegfried Müller. A Central Scheme for Two Coupled Hyperbolic Systems[J]. Communications on Applied Mathematics and Computation, 2024, 6(4): 2093-2118.

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A Central Scheme for Two Coupled Hyperbolic Systems

A Central Scheme for Two Coupled Hyperbolic Systems

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