Water and Hydrogen Flow in Networks: Modelling and Numerical Solution by ROW Methods

This chapter deals with the simulation of infrastructure networks for water and gas. Examples, covered with this chapter, are water supply or disposal networks as well as natural gas or hydrogen networks. First, a general modelling approach using nodes and directed edges is presented and described for selected network elements. The mathematical description of the individual elements leads to coupled linear and nonlinear algebraic equations, and to ordinary and partial differential equations. A large system of differential-algebraic equations (DAEs) is generated by appropriate space discretizations of the hyperbolic conservation equations. In three test examples the numerical solution of these DAEs is considered. It is shown that Rosenbrock-Wanner (ROW) methods are very well suited for this type of DAE problems generated by network modelling. Although they are not the fastest methods in all cases, they prove to be very robust and therefore good candidates for software used in the control rooms of network operators.