An implicit method for transient gas flows in pipe networks

Abstract

This paper describes a fully implicit finite-difference method for calculating the unsteady gas flow in pipeline networks. The algorithm for solving the finite-difference equations of a pipe is based on the Newton-Raphson method. The Von Neumann stability analysis on the finite-difference equations of a pipe shows that the equations are unconditionally stable. An iterative convergence method is applied to the calculation of node pressure at junctions in networks. The parameter study on the convergence shows that the stability depends on the convergence tolerance. Calculation results of a few sample cases are compared with those of the method of characteristics and the two-step Lax-Wendroff method. An excellent agreement between the methods is obtained when a small time step is used. Computation time can be greatly reduced by using the implicit method.