• DOI:10.1007/s10955-016-1529-5
• Corpus ID: 117357645

Moment Closure Approximations of the Boltzmann Equation Based on $$\varphi $$φ-Divergences

@article{Abdelmalik2015MomentCA,
  title={Moment Closure Approximations of the Boltzmann Equation Based on \$\$\varphi \$\$$\phi$-Divergences},
  author={M. R. A. Abdelmalik and E. H. van Brummelen},
  journal={Journal of Statistical Physics},
  year={2015},
  volume={164},
  pages={77-104}
}

• M. Abdelmalik, E. H. Brummelen
• Published 17 March 2015
• Mathematics
• Journal of Statistical Physics

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 $$\varphi $$φ-divergences and a corresponding closure procedure based on minimization of $$\varphi $$φ-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.