On total variation diminishing schemes for pressure transients

A higher-order numerical procedure is applied to simulate typical transient phenomena in natural gas transportation. Reliable modeling and prediction of transients features in transmission pipelines are desirable for optimal control of gas deliverability, design and implementation of active controls, and modeling of operational behavior of network peripheral equipment (e.g., chokes, valves, compressors, etc.). As an alternative to the method of characteristics (MOC) that has been widely used for modeling these systems, higher-order total variation diminishing (TVD) methods are used to model some transient problems. This class of methods has the capability of capturing fine-scale phenomena, and they do provide a better resolution of frontal discontinuities. In this study, the TVD schemes are utilized in conjunction with upwind methods. Also, in order to ensure a stable time-stepping scheme over a wide range of Courant-Friedrich-Lewy (CFL) number, a special Runge-Kutta method is employed as the base solution algorithm to integrate the highly nonlinear, hyperbolic equations which govern the transportation of natural gas in pipelines. The overall procedure is stable, robust, and accurate when applied to solve practical problems with dynamic pressure waves.