A Numerical Method for a Reformulated Nonlinear Gas Transmission Model

This paper presents a mathematical and computational method for approximating the solution of nonlinear gas transmission systems, with application to the Irish gas network. Starting from the governing partial differential equations, we derive a steady-state formulation under equilibrium assumptions, leading to a system of nonlinear algebraic equations. To approximate the solution efficiently, we propose a tailored method in which we use a physically informed estimate and construct a linear system whose solution closely approximates the nonlinear model. This approach enables fast computation of steady-state pressures and flows and provides a practical tool for gas network analysis. A numerical example illustrates the effectiveness of the method under realistic conditions.