@article{DomschkeDuaStolwijketal.2017, author = {Domschke, Pia and Dua, Aseem and Stolwijk, Jeroen J. and Lang, Jens and Mehrmann, Volker}, title = {Adaptive Refinement Strategies for the Simulation of Gas Flow in Networks using a Model Hierarchy}, volume = {Electronic Transactions on Numerical Analysis}, number = {Vol. 48}, doi = {10.1553/etna_vol48s97}, pages = {97 -- 113}, year = {2017}, 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.}, language = {en} }