| Abstract: | The mathematical model describing transients in natural gas pipelines constitutes a non‐homogeneous system of non‐linear hyperbolic conservation laws. The time splitting approach is adopted to solve this non‐homogeneous hyperbolic model. At each time step, the non‐homogeneous hyperbolic model is split into a homogeneous hyperbolic model and an ODE operator. An explicit 5‐point, second‐order‐accurate total variation diminishing (TVD) scheme is formulated to solve the homogeneous system of non‐linear hyperbolic conservation laws. Special attention is given to the treatment of boundary conditions at the inlet and the outlet of the pipeline. Hybrid methods involving the Godunov scheme (TVD/Godunov scheme) or the Roe scheme (TVD/Roe scheme) or the Lax–Wendroff scheme (TVD/LW scheme) are used to achieve appropriate boundary handling strategy. A severe condition involving instantaneous closure of a downstream valve is used to test the efficacy of the new schemes. The results produced by the TVD/Roe and TVD/Godunov schemes are excellent and comparable with each other, while the TVD/LW scheme performs reasonably well. The TVD/Roe scheme is applied to simulate the transport of a fast transient in a short pipe and the propagation of a slow transient in a long transmission pipeline. For the first example, the scheme produces excellent results, which capture and maintain the integrity of the wave fronts even after a long time. For the second example, comparisons of computational results are made using different discretizing parameters. Copyright © 2000 John Wiley & Sons, Ltd. |
