An iterative method for solving nonlinear equations of real gas pipeline transport

Abstract

The study is devoted to the development of a numerical method to solve the equations of pipeline transport of compressible gas, taking into account the forces of resistance, gravity, local and convective components of the gas inertia force in the isothermal mode of factors. The power of the unknowns in the momentum conservation equation is reduced with the introduction of the auxiliary function of natural logarithm of the reduced density. Autonomous equations of linear combinations of the hydrodynamic flow rate and a newly introduced function were compiled with the participation of the propagation velocity of small pressure disturbances. In this paper, an iterative method is developed to solve equations for the implementation of the input condition for pressure and output condition for mass flow; it allows determining the unknown boundary and internal values of gas-dynamic parameters. The results of a computational experiment on the route change in flow indices at various slopes of the gas pipeline route are analyzed.