  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.
