A finite difference method for set of nonlinear partial differential equations of natural gas flow in transmission pipeline
Subject Areas : International Journal of Industrial Mathematicshamed ameri 1 * , mahmood farzaneh-gord 2
1 - Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran
2 - Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran
Keywords: pipeline, finite difference, Newton-Raphson, natural gas,
Abstract :
This paper deals with natural gas flow equations and numerical simulation of gas transmission pipeline. This flow is described by the continuity, momentum, and energy equations along with a state equation. In this project we use the implicit finite difference method that requires using the Newton-Raphson method to solve a set of nonlinear simultaneous equations at each time step. by using this method, partial differential equations transform to algebraic equations.