An Implicit Method for Transient Flow in Pipe Networks

Abstract

This paper describes a fully implicit finite-difference method for calculating unsteady gas flow in pipeline networks. The algorithm for solving the finite-difference equations of a pipe is based on the iterative Newton-Raphson method. The standard Neumann stability analysis of the finite-difference equations of a pipe shows that the equations are unconditionally stable. For the calculation of node pressure at junctions in networks, an iterative convergence method is applied. Studies on the convergence are performed parametrically. The result 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 is obtained in a small time step. Computation time can be reduced by the method. © 1993, The Japan Society of Mechanical Engineers. All rights reserved.