## 1 Introduction  
The continuous uninterrupted supply of Natural Gas (NG) is crucial to today's economy. The balancing of gas supply from a wide range of sources with various end users can be challenging due to the unique and different behaviours of the end users, which in some cases span across a continent [1, 2]. NG is one of the strategic primary sources of energy in the world, supplying approximately 24% of the world's primary energy in 2016 [3]. This increases to 30% in Ireland, where on occasion, 80% of peak power demand is provided by NG [4], and in Singapore, where generated electricity can be up to 95% [5] from NG. Transport of NG via pipeline is the most efficient and economic and has the lowest carbon footprint [6, 7, 8], and in many instances, the gas network is capable of supplying NG from gas fields directly to the end users (from Well to Wheels; WtW is a common expression for the life cycle of a product). A gas network includes both transmission and distribution pipelines, compressor stations to bring the transmission network to its operating pressure and CityGas reduction Stations (CGS) and Town Break Stations (TBS) to reduce the NG pressure so that it can be provided safely into homes and business [9]. Gas systems need a reliable design to ensure effective operation, and due to the important role of natural gas of supplying primary energy and the significant investment in the network infrastructure, using a reliable and fast method for solving the gas flow calculations is essential. Gas network simulation allows for the understanding and forecast of the behaviour of the gas network under different conditions, and it is useful for decision makers for installing an optimal system. For the simulation of a gas network, the pipe flow equations that describe the flow, pressure, compressibility, line-pack capacity, and density of the compressible gas in the pipelines need to be solved. These equations include variables dependant on the gas composition, temperature, pipe length and diameter, gas constant, and pipe inclination, along with unknown variables such as pressure and flow rate. The pressure and flow rate are the most important variables from all points of view including financial/trading, technical, environmental, and health and safety. Gas network simulation helps the Transmission System Operator (TSO) understand how the individual components work together as a system. It is crucial in planning for the development and expansion of the network, the prevention of faults due to system changes in supply or demand nodes [2], and in managing crisis events that occur due to catastrophic component failures. Furthermore, deviations between accurate simulations and measured parameters can be an indication of leakage, which is important not just due to lost revenue point of view, but also from an environmental [10; 11] and worker safety point of view. Therefore, accuracy is hugely important for simulations, where it can be the difference between making a profit or loss for both the TSO and the retailer [12]. Validation of the simulations requires reliable data, and robust reliable metering devices are key to ensuring this; they are also crucial in custody transfer, which is becoming more important as gas markets are opening up. Multiple variables affect gas flow through a pipeline, all of which must be accounted for in the modelling of the gas network; these are pressure, flow rate, density, comparability, friction factors, inclination of the pipe, the Reynolds number, gas velocity, and pipe length and diameter. The most important variable in a gas network is pressure, which is the driving force for the transport of the NG through the pipe. When gas flows, the pressure decreases due to the frictional interaction between the gas and the pipe wall, exerting a shear force on the gas [2; 13; 14; 15; 16; 17]. The modelling of the network topology also needs to be accounted for as it affects the gas pressure and has a major impact on the energy required to pump gas through the network.