Moment closure approximations of the Boltzmann Equation based on {\phi}-divergences

• Main Authors: Abdel-Malik, M. R. A, van Brummelen, E. H
• Format: Journal Article
• Language: English
• Published: 17.03.2015
• Subjects: Mathematics - Mathematical Physics; Physics - Computational Physics; Physics - Mathematical Physics
• DOI: 10.48550/arxiv.1503.05183

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.