1885 eng reportzib 0 2013-07-01 2013-07-01 -- We consider a nonlinear nonconvex network flow problem that arises, for example, in natural gas or water transmission networks. Given is such network with active and passive components, that is, valves, compressors, pressure regulators (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes of the network. Besides flow conservation constraints in the nodes the flow must fulfill nonlinear nonconvex pressure loss constraints on the arcs subject to potential values (i.e., pressure levels) in both end nodes of each arc. The problem is how to numerically compute this flow and pressures. We review an existing approach of Maugis (1977) and extend it to the case of networks with active elements (for example, compressors). We further examine different ways of relaxations for the nonlinear network flow model. We compare different approaches based on nonlinear optimization numerically on a set of test instances. urn:nbn:de:0297-zib-18857 Armin Fügenschuh Armin Fügenschuh Jesco Humpola 13-31 eng uncontrolled Nonlinear Network Flow eng uncontrolled Mixed-Integer Nonlinear Programming eng uncontrolled Relaxations OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING Mathematical Optimization Fügenschuh, Armin MODAL-GasLab ForNe MODAL-Gesamt Applied Optimization https://opus4.kobv.de/opus4-zib/files/1885/ZR-13-31.pdf