Networks of hyperbolic PDEs arise in different applications, e.g. modeling water- or gas-networks or road traffic. In the first part of this talk we discuss modeling aspects of coupling conditions for hyperbolic PDEs.

Starting from an kinetic description we derive coupling conditions for the associated macroscopic equations. For this process a detailed description of the boundary layer is important. In the second part appropriate numerical methods are considered.

Different high order approaches are compared and applications to district heating or water networks are discussed.