16:00 - 17:00
Title: Control problems and stability of hierarchical moment models for fluid dynamics
Abstract: Applications of atmospheric re-entry and geophysical flows are characterized by a large variety of separate models for specific tasks. This model variety poses significant difficulties both for the analysis and for the numerical solution. We thus need to rethink mathematical modelling for future numerical simulations. In this talk, I will introduce hierarchical moment models as a flexible way to derive hierarchies of models in fluid dynamics and other applications. The general derivation procedure results in structural similarities of the models, which facilitate physical insight, model adaptivity, and the development of suitable numerical methods. Based on rarefied gases and shallow flows, I will exemplify the hierarchical moment approach and highlight runtime and accuracy improvements. From a control theory perspective, I will discuss problems for the future extension towards adaptive self-learning models that make use of the hierarchical structure of the models. Lastly, I will discuss the derivation and stability analysis of a hierarchical model for a linear delay differential equation with uncertain parameters.