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Preprint 03-2017

Adaptive Refinement Strategies for the Simulation of Gas Flow in Networks using a Model Hierarchy

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Author(s) : Pia Domschke , Aseem Dua , Jeroen J. Stolwijk , Jens Lang , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 03-2017

MSC 2000

65K99 None of the above, but in this section
65Z05 Applications to physics

Abstract :
A model hierarchy that is based on the one-dimensional isothermal Euler equations of fluid dynamics is used for the simulation and optimisation of 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.

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

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