Volume 48, pp. 97-113, 2018.

Adaptive refinement strategies for the simulation of gas flow in networks using a model hierarchy

Pia Domschke, Aseem Dua, Jeroen J. Stolwijk, Jens Lang, and Volker Mehrmann


A model hierarchy that is based on the one-dimensional isothermal Euler equations of fluid dynamics is used for the simulation and optimisation of natural gas flow through a pipeline network. Adaptive refinement strategies have the aim of bringing the simulation error below a prescribed tolerance while keeping the computational costs low. While spatial and temporal stepsize adaptivity is well studied in the literature, model adaptivity is a new field of research. The problem of finding an optimal refinement strategy that combines these three types of adaptivity is a generalisation of the unbounded knapsack problem. A refinement strategy that is currently used in gas flow simulation software is compared to two novel greedy-like strategies. Both a theoretical experiment and a realistic gas flow simulation show that the novel strategies significantly outperform the current refinement strategy with respect to the computational cost incurred.

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Key words

gas supply networks, model hierarchy, error estimators, model adaptivity, refinement strategies

AMS subject classifications

65K99, 65Z99, 65M22, 35Q31

ETNA articles which cite this article

Vol. 54 (2021), pp. 392-419 Martin Stoll and Max Winkler: Optimal Dirichlet control of partial differential equations on networks

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