%0 Journal Article
%T Moment closure approximations of the Boltzmann Equation based on ¦Õ-divergences
%A M. R. A. Abdel-Malik
%A E. H. van Brummelen
%J Physics
%D 2015
%I arXiv
%X This paper is concerned with approximations of the Boltzmann equation based on the method of moments. We propose a generalization of the setting of the moment-closure problem from relative entropy to {\phi}-divergences and a corresponding closure procedure based on minimization of {\phi}-divergences. The proposed description encapsulates as special cases Grad's classical closure based on expansion in Hermite polynomials and Levermore's entropy-based closure. We establish that the generalization to divergence-based closures enables the construction of extended thermodynamic theories that avoid essential limitations of the standard moment-closure formulations such as inadmissibility of the approximate phase-space distribution, potential loss of hyperbolicity and singularity of flux functions at local equilibrium. The divergence-based closure leads to a hierarchy of tractable symmetric hyperbolic systems that retain the fundamental structural properties of the Boltzmann equation.
%U http://arxiv.org/abs/1503.05183v1