AbstractThe operation of gas pipeline flow with high pressure and small Mach numbers allows to model the flow by a semilinear hyperbolic system of partial differential equations. In this paper we present a number of transient and stationary analytical solutions of this model. They are used to discuss and clarify why a PDE model is necessary to handle certain dynamic situations in the operation of gas transportation networks. We show that adequate numerical discretizations can capture the

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... al behavior sufficiently accurate. We also present examples that show that in certain cases an optimization approach that is based on multi-period optimization of steady states does not lead to approximations that converge to the optimal state.