Numerical modeling transient processes in a long gas pipeline

Unsteady processes of isothermal natural gas flow, emerging in a long pipeline when there is switching-over from one stationary process to another stationary process, have been considered in this paper.  The one-dimensional system of gas dynamics equations is used for that purpose.  It includes equations for conservation of mass and momentum written relative to of dimensionless mass and flow densities.  Three boundary-value problems formulated for this system define three models for control of the transient processes.  The problems differ by the boundary (control) functions imposed at the ends of the gas pipeline.  A unified model for the control functions is introduced.  According to this model, such a function is defined by four real parameters.  That restricts the class of control functions by the smooth ones monotonically varying from the value characteristic for the first stationary regime to the other one specific for the second stationary regime.  The transient processes realized with the use of the models for various values of control parameters are analyzed numerically in this paper.  Application of the considered mathematical models and obtained results of conducted case-studies for planning the transient regimes of pipelines operation are discussed in the paper.