  We propose an adaptive optimization algorithm for operating district heating
networks in a stationary regime. The behavior of hot water flow in the pipe
network is modeled using the incompressible Euler equations and a suitably
chosen energy equation. By applying different simplifications to these
equations, we derive a catalog of models. Our algorithm is based on this
catalog and adaptively controls where in the network which model is used.
Moreover, the granularity of the applied discretization is controlled in a
similar adaptive manner. By doing so, we are able to obtain optimal solutions
at low computational costs that satisfy a prescribed tolerance w.r.t. the most
accurate modeling level. To adaptively control the switching between different
levels and the adaptation of the discretization grids, we derive error measure
formulas and a posteriori error measure estimators. Under reasonable
assumptions we prove that the adaptive algorithm terminates after finitely many
iterations. Our numerical results show that the algorithm is able to produce
solutions for problem instances that have not been solvable before.
