Well-balanced scheme for gas-flow in pipeline networks

Gas flow through pipeline networks can be described using \begin{document}$ 2\times 2 $\end{document} hyperbolic balance laws along with coupling conditions at nodes. The numerical solution at steady state is highly sensitive to these coupling conditions and also to the balance between flux and source terms within the pipes. To avoid spurious oscillations for near equilibrium flows, it is essential to design well-balanced schemes. Recently Chertock, Herty & Ozcan[ 11 ] introduced a well-balanced method for general \begin{document}$ 2\times 2 $\end{document} systems of balance laws. In this paper, we simplify and extend this approach to a network of pipes. We prove well-balancing for different coupling conditions and for compressors stations, and demonstrate the advantage of the scheme by numerical experiments.