Asymptotic waves and shock formation in a gas flowing in a long pipeline

We present a numerical study of a fluid flow through a long pipeline which undergoes a perturbation. The theory of asymptotic waves predicts the arising of discontinuities in the field functions and this event is widely believed to be strictly related to shock waves formation. This phenomenon may be of some relevance during the transfer of industrial gases through a network of pipelines for their intrinsic potential hazard. As is known, the industrial transport of fluids such as natural or flammable gases, operates generally at high pressure and low velocity, and this means that small segments of a pipeline may contain a large mass of fluid. The shock formation develops after only a finite distance of propagation and in times of the order of few seconds. In this work we test the theory by considering a sample of flow models.