Topological solvability analysis and its application to liquid flow networks coupled to Functional Mock-up Units

We present a unified topological analysis for physical networks coupled to black-box models. While the governing equations of the physical network are derived by representing the network as a linear graph, the equations of the black-box model are characterized as an abstract class of Differential-Algebraic equations (DAEs) of a specific form (Functional Mock-up Unit). Combining those two representations, existence and uniqueness results can be formulated based on the connectivity of the physical network and a concrete classification of the black-box models. This is the natural extension of the approach derived in [3].