A Framework on Moment Model Reduction for Kinetic Equation

TL;DR

This paper introduces a unified framework for model reduction of kinetic equations, revealing the reasons behind hyperbolic regularization success and enabling the discovery of new hyperbolic models.

Contribution

It provides a general approach to reduce kinetic equations to moment systems, explaining hyperbolic regularization and facilitating the creation of novel models.

Findings

Revealed the underlying reason for hyperbolic regularization effectiveness.

Represented existing models and discovered new hyperbolic models through routine calculations.

Deduced a new globally hyperbolic model within Grad's 13-moment system scope.

Abstract

By a further investigation on the structure of the coefficient matrix of the globally hyperbolic regularized moment equations for Boltzmann equation in [Z. Cai, Y. Fan and R. Li, Comm. Math. Sci., 11 (2013), pp. 547-571], we propose a uniform framework to carry out model reduction to general kinetic equations, to achieve certain moment system. With this framework, the underlying reason why the globally hyperbolic regularization in [Z. Cai, Y. Fan and R. Li, Comm. Math. Sci., 11 (2013), pp. 547-571] works is revealed. The even fascinating point is, with only routine calculation, existing models are represented and brand new models are discovered. Even if the study is restricted in the scope of the classical Grad's 13-moment system, new model with global hyperbolicity can be deduced.