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

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