A Relaxation Method for the Coupling of Systems of Conservation Laws

The present work investigates the spatial coupling of different hyperbolic models, from the theoritical and numerical points of view. The problem of coupling often occurs in an industrial context. Consider a complex system, such as a nuclear reactor. Different phenomena can appear according to the region and thus, different models (and numerical methods) are used. The difficulty lies in letting the different models communicate, since they are not necessarily compatible. Hence we study the spatial coupling of two different hyperbolic systems of conservation laws through the interface {x = 0}: