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The stable operation of gas networks is an important optimization target.While for this task commonly finite volume methods are used, we introduce a newfinite difference approach. With a summation by part formulation for thespatial discretization, we get well-defined fluxes between the pipes. Thisallows a simple and explicit formulation of the coupling conditions at thenode. From that, we derive the adjoint equations for the network simply andtransparently. The resulting direct and adjoint equations are numericallyefficient and easy to implement. The approach is demonstrated by theoptimization of two sample gas networks.

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