Calculation of transient fluid flow regimes in pipeline networks

We consider the calculation problem of flow regimes of transient processes in oil pipeline networks of complicated loop-back structure. The fluid flow in each linear pipe is described by a system of two first-order linear hyperbolic partial differential equations. At the junctions of the network, there are fulfilled unseparated boundary conditions determined by the first Kirchhoff law and by the continuity of the flow. We propose a scheme for the numerical solution to the problem based on the application of the grid method and obtain formulas that are an analog of the sweep method and do not depend on the number of junctions, pipes, and the structure of the pipeline network. Numerical experiments applying the proposed approach are implemented, some analysis of the results is carried out.