Abstract. The problem of finding the parameters of the gas transmission system in terms of its operation under unsteady operating modes are considered. We show mathematical models of gas flows in the basic facilities in the system with a complicated piping diagram. The solution is built to solve a system of partial differential equations with the finite element method of large dimension with boundary conditions, some of which are designed in the process of solving the system of equations. This is due to the provision of technical and technological constraints on the pressure of the controlled points of the system. On the resistance to finding a solution significantly affects a step of the time coordinate. The proposed algorithm in the editing process of flow diagrams provides an increase in stability of solving systems of equations, and significantly reduces the time for the simulation.
Key words: transmission system, compressor station, optimal operating mode, gas flow model, network model, piping diagram, finite element method.