  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.
