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

TL;DR

This paper introduces a finite difference method for simulating and optimizing gas networks, offering a simpler, explicit approach that improves efficiency and ease of implementation over traditional finite volume methods.

Contribution

The paper presents a novel finite difference approach with summation by parts for gas network simulation and adjoint optimization, simplifying coupling conditions and adjoint derivation.

Findings

Efficient and easy-to-implement simulation and optimization of gas networks.

Demonstrated effectiveness on two sample networks.

Provides a new alternative to finite volume methods.

Abstract

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. The approach is demonstrated by the optimization of two sample gas networks.