This paper proposes a method of solving steady flows in large pipelines with the transient analysis (MOC) combined with the network analysis. The existing methods of accelerating the speed of convergence to steady flows in pipelines, i.e., the time marching approach (TMA) replaces the system dimensions (lengths of pipes, friction factors, wave speeds) by not actual ones and dynamically controls one optimization parameter to reduce the spectral radius. That method will be applied to two pipeline systems having a few thousand of pipes. To accelerate much more the convergence the graph-theoretical information used in the network analyses is implemented. From the discharges computed with TMA the heads at each node are adequately modified using the information of “Tree” of the directed-graph defined for pipelines. Two variations of the method are also proposed. They reduces much the Cpu time to solve steady flows in large pipelines.

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