Solution for Solving Dynamic Partial Differential Equation Model of Natural Gas Pipeline Network Based on Discretization and Linearization

This study proposes a discretization and linearization method for the dynamic PDE model of the gas transmission network to address the challenge of effectively balancing calculation speed and solution accuracy in current methods for solving the dynamic partial differential equations (PDEs) of the gas transmission network. Initially, it uses the finite volume method (FVM) and the finite difference method (FDM) to derive the discretized and linearized gas pipeline PDEs with high precision. Then, this research introduces a fast solution scheme based on the SIMPLE algorithm to address the complex problem of calculating large-scale discretized equations. For the equations at each discrete grid node, a solution equation format to reduce the variable scale is derived and is solved through the “assumption–correction” approach to enhance solution accuracy. Employing the results from the commercial software Pipeline Studio as a benchmark, the proposed method is applied to the dynamic simulation cases of a single pipeline and a simple pipeline network, respectively. The solution speed and accuracy are then compared to those of the FDM, characteristic method (CM), and energy circuit theory (ECT). In each case, the impact of different space steps on the accuracy and speed of the proposed method and other methods is explored. The results indicate that the average error of the proposed method was 0.194 3% when solving a single pipeline model, with a solution time of 1.169 seconds. The average error in the simulation of a simple pipeline network is 0.279 4%, and the time is 37.285 seconds. In addition, the proposed method ensures convergence with various space steps, maintaining an average error within 0.3%. This case demonstrates the stability of the proposed method, confirming that the speed and accuracy requirements can be fully met and effectively applied in the dynamic simulation research of natural gas transmission pipeline networks.