Model Order Reduction and Moment Models for Rarefied Gases
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The high computational complexity of many approaches to simulate rarefied gases requires model order reduction techniques to achieve accurate numerical solutions. In fact, an accurate solution of the full model is often not necessary, as only a smaller set of variables suffices to characterise the main behaviour of the solution. This poses the question of efficient model reduction: How can we efficiently reduce the complexity of the model and arrive at a reduced model, that is both sufficiently accurate and computationally feasible? In this talk, we fist briefly discuss different model reduction techniques for kinetic equations. We then focus on moment models as one way to reduce the full model to a set of analytical, lower-dimensional equations. The benefits of moment models are the mathematically sound derivation, their hierarchical structure, and the possibility to assess analytical properties of the model from the resulting equations.