Hrsg.: Fraunhofer ITWM
2022, 151 S., num., col. illus. and tab., Softcover
This thesis tackles the modeling and efficient simulation of district heating networks. The dynamical behavior of water in the pipes is described by the incompressible Euler equations. Conservation of the involved quantities determines the coupling at each junction in the network, leading to a system of partial differential algebraic equations. For that system, the unique existence of a solution is shown. Furthermore, a stability estimate for the dependence on important parameters is derived. A new local time stepping algorithm is presented that is perfectly suited for the solution of the transport problem involved. In comparison to generic high order ADER schemes its high efficiency outperforms the classical approach significantly. In order to enable computation of vary large time steps, implicit methods are investigated. A high order finite volume method is equipped with an a posteriori limiter. The superior behavior of the constructed hybrid scheme is shown in different numerical tests and applications. The obtained results build an important foundation for the upcoming optimization problems.