Finite-difference-based simulation and adjoint optimization of gas networks

The stable operation of gas networks is an important optimization target. While for this task commonly finite volume methods are used, we introduce a new finite difference approach. With a summation by part formulation for the spatial discretization, we get well-defined fluxes between the pipes. This allows a simple and explicit formulation of the coupling conditions at the node. From that, we derive the adjoint equations for the network simply and transparently. The resulting direct and adjoint equations are numerically efficient and easy to implement.