I am new to understanding the transient and steady state analysis of the natural gas pipeline grids. Are there any articles/textbooks that can be suggested which explain about the steady state and transient nature, the gas flow differential equations and how to discretize them?
A transient state is where the flow of gas changes with time, but a steady state does not. However, one must also account for STABLE and UNSTABLE steady states as well. A stable steady state is one in which the gas flow will always return to its original state after a perturbation, but an unstable steady state is an example of gas flow which does not, but effectively diverges. A mathematical example of a STABLE steady state is a STABLE NODE or a STABLE SPIRAL and an UNSTABLE steady state may be illustrated by an UNSTABLE NODE, an UNSTABLE SPIRAL, or a SADDLE POINT. There are many text books that discuss such concepts, but Jordan and Smith is a good start regarding how to plot the phase diagrams that contain such nodes, spirals, and saddle points. There are also countless Physics books that will discuss the fluid dynamics aspect of the subject, such as Bernoulli's equation for fluids and gases flowing through pipes, but I am unsure of the best ones to cite here myself as I am not a physicist.
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