In this talk, I will give an overview of entropy-based moment closures and present some analysis concerning the issue of realizability in the context of gas dynamics. Entropy-based moment closures for kinetic equations have received significant attention in the past several years.
These closures, which are formulated as the solution of a convex functional related the kinetic entropy, generate systems of hyperbolic PDE which formally inherit some fundamental features of the underlying kinetic description, such as an H-Theorem that characterizes the trend to local equilibrium. This makes the entropy-based methodology an attractive tool for simulating kinetic models in transition regimes. Unfortunately, entropy-based closures are very ill-conditioned, in the sense that the relationship between given set of moments and the expansion coefficients used in the closure ansatz is typically very hard to compute.
Furthermore, in some cases, physically relevant moments can not even be generated by the entropy ansatz. This is exactly the realizability problem which I will discuss in some detail.
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