Topological solvability and DAE-index conditions for mass flow controlled pumps in liquid flow networks: RICAM-Report 2016-33

This work is devoted to the analysis of a model for the thermal management in liquid flow networks consisting of pipes and pumps. The underlying model equation for the liquid flow is not restricted to the equation of motion and the continuity equation, describing the mass transfer through the pipes, but also includes thermodynamic effects in order to cover cooling and heating processes. The resulting model gives rise to a differential-algebraic equation (DAE), for which a proof of unique solvability and an index analysis is presented. For the index analysis, the concepts of the Strangeness Index is pursued. Exploring the network structure of the liquid flow network via graph theoretical approaches allows to develop network topological criteria for the existence of solutions and the DAE-index. The topological criteria are explained by various examples.