Cooling as well as heating circuits can be modeled as a network of elements that obey mass, momentum, and energy balance laws. Typical elements in such circuits are pipes, regulated pumps, regulated (multi-way) valves, and energy exchangers. For these elements, we give an overview of the modeling process including the basics of the continuum mechanics of fluids, together with simplifying assumptions that are practically acceptable. Moreover, we consider the modeling of network domains and the numerical treatment of the problem. The overview is designed for a reader interested in the implementation of the presented methods. We also address deep coupling of the simulation with optimization algorithms. For this purpose, we show how a model needs to be set up in order for Newton-type solvers and interior point methods to be applicable to it. The introduction of the model is complemented in (T. Clees et al., Scientific Computing and Algorithms in Industrial Simulations. Springer, Cham, 2017) by a very detailed case study conducted on a real system, being part of a supercomputing center.
