534 RWTH Publication No: 958596        2023       
TITLE A central scheme for two coupled hyperbolic systems
AUTHORS Michael Herty, Niklas Kolbe, Siegfried Müller
ABSTRACT A novel numerical scheme to solve coupled systems of conservation laws is intro- duced. 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 behavior 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, 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.
KEYWORDS Coupled conservation laws; hyperbolic systems, finite-volume schemes; cou- pling conditions; relaxation system
DOI 10.1007/s42967-023-00306-5
PUBLICATION accepted for publication in Communications on Applied Mathematics and Computation