SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2143-2171, October 2024.
Abstract. The coupling of nonconservative hyperbolic systems at a static interface has been a delicate issue as common approaches rely on the Lax-curves of the systems, which are not always available. To address this a new linear relaxation system is introduced, in which a nonlocal source term accounts for the nonconservative product of the original system. Using an asymptotic analysis the relaxation limit and its stability are investigated in the uncoupled setting. It is shown that the path-conservative Lax–Friedrichs scheme arises from a discrete limit of an implicit-explicit scheme for the relaxation system. Employing the relaxation approach, a novel technique to couple two nonconservative systems under a large class of coupling conditions is established. A particular coupling strategy motivated from conservative Kirchhoff conditions is introduced and a corresponding Riemann solver provided. A fully discrete scheme for coupled nonconservative products is derived and studied in terms of path conservation. Numerical experiments applying the approach to a coupled model of vascular blood flow are presented.

中文翻译：

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非保守双曲方程耦合系统的数值方案


《SIAM 数值分析杂志》，第 62 卷，第 5 期，第 2143-2171 页，2024 年 10 月。

抽象的。静态界面上非保守双曲系统的耦合一直是一个棘手的问题，因为常见的方法依赖于系统的 Lax 曲线，而该曲线并不总是可用。为了解决这个问题，引入了一种新的线性松弛系统，其中非局部源项解释了原始系统的非保守乘积。使用渐近分析，在非耦合设置中研究松弛极限及其稳定性。结果表明，路径保守的 Lax-Friedrichs 格式源自松弛系统的隐式-显式格式的离散极限。采用松弛方法，建立了一种在一大类耦合条件下耦合两个非保守系统的新技术。引入了一种基于保守基尔霍夫条件的特殊耦合策略，并提供了相应的黎曼求解器。从路径守恒的角度推导并研究了耦合非保守乘积的完全离散方案。提出了将该方法应用于血管血流耦合模型的数值实验。