A new linear relaxation system for nonconservative hyperbolic systems 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. It is shown that the path-conservative Lax-Friedrichs scheme arises from a discrete limit of an implicit-explicit scheme for the relaxation system. The relaxation approach is further employed to couple two nonconservative systems at a static interface. A 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.

翻译：本文介绍了一种针对非守恒双曲型系统的新型线性松弛系统，其中非局部源项用于描述原始系统中的非守恒乘积。通过渐近分析，研究了松弛极限及其稳定性。结果表明，路径守恒的Lax-Friedrichs格式源于松弛系统的隐式-显式格式的离散极限。进一步将松弛方法应用于静态界面处两个非守恒系统的耦合问题。基于保守型基尔霍夫条件提出了耦合策略，并提供了相应的黎曼求解器。推导并研究了针对耦合非守恒乘积的全离散格式，从路径守恒角度进行了分析。通过血管血流耦合模型的数值实验验证了该方法。