Model Reduction of Kinetic Equations by Operator Projection

TL;DR

This paper introduces a unified operator projection framework for deriving globally hyperbolic moment systems from kinetic equations, simplifying the process and encompassing existing and new models.

Contribution

A concise, algorithmic framework for deriving hyperbolic moment systems from kinetic equations, including existing and novel models.

Findings

Framework includes almost all existing hyperbolic moment systems.

Can derive new regularized and multidimensional moment systems.

Simplifies and unifies the derivation process.

Abstract

By a further study of the mechanism of the hyperbolic regularization of the moment system for Boltzmann equation proposed in [Z. Cai, Y. Fan, R. Li, Comm. Math. Sci. 11(2): 547-571, 2013], we point out that the key point is treating the time and space derivative in the same way. Based on this understanding, a uniform framework to derive globally hyperbolic moment systems from kinetic equations using an operator projection method is proposed. The framework is so concise and clear that it can be treated as an algorithm with four inputs to derive hyperbolic moment system by routine calculations. Almost all existing globally hyperbolic moment system can be included in the framework, as well as some new moment system including globally hyperbolic regularized versions of Grad ordered moment system and a multidimensional extension of the quadrature-based moment system.