A Central Scheme for Two Coupled Hyperbolic Systems

Michael Herty; Niklas Kolbe; Siegfried Müller

doi:10.1007/s42967-023-00306-5

Communications on Applied Mathematics and Computation ›› 2023, 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

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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.

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Michael Herty, Niklas Kolbe, Siegfried Müller. A Central Scheme for Two Coupled Hyperbolic Systems. Communications on Applied Mathematics and Computation, 2023, 6(4): 2093-2118 DOI:10.1007/s42967-023-00306-5