The objective of mesh and model adaptation is to locally choose the mesh and the model to be employed from a model hierarchy in order to reduce the computational resources needed. We do this by balancing the two sources of error, namely discretization and modelling error. In this work, we devise a mesh and model adaptation strategy for a class of model hierarchies consisting of two levels of model complexity. In particular, the fine model, also referred to as the complex system, consists of a system of hyperbolic balance laws with stiff reaction terms and the coarse model, also referred to as the simple system, consists of a system of hyperbolic conservation laws. The governing equations of the simple system are derived by making a simplifying assumption that the system is in equilibrium, i.e. the speed of the reaction is infinitely fast. Furthermore, the complex system is assumed to have an entropy structure, i.e. it is assumed to be equipped with a strictly convex entropy and entropy flux. The structure of the model hierarchy allows us to show that the simple system is analogously equipped with a strictly convex entropy and entropy flux. The relative entropy stability framework is employed to derive a posteriori error estimates with identifiable contributions of discretization and modelling error estimates. Furthermore, since the use of two different models in the computational domain gives rise to cell boundaries across which the model employed differs, we propose a coupling to be employed at these cell boundaries. In addition, mesh and model coarsening distances are defined, which provide complementary information to the defined error indicators. The defined error indicators and coarsening distances are employed to propose a mesh and model adaptation strategy. The efficacy of the mesh and model adaptation strategy is demonstrated by conducting simulations for chemically reacting fluid mixtures in one space dimension.

https://tuprints.ulb.tu-darmstadt.de/23048