Hierarchical Modelling and Model Adaptivity for Gas Flow on Networks

We are interested in simulation and optimization of gas transport in networks. Different regions of the network may be modelled by different equations: There are three models based on the Euler equations that describe the gas flow in pipelines qualitatively different: a nonlinear model, a semilinear model and a stationary also called algebraic model. For the whole network, adequate initial and boundary values as well as coupling conditions at the junctions are needed. Using adjoint techniques one can specify model error estimators for the simplified models. A strategy to adaptively apply the different models in different regions of the network while maintaining the accuracy of the solution is presented.