Hyperbolic Model Reduction for Kinetic Equations

Abstract

We make a brief historical review of the moment model reduction for the kinetic equations, particularly Grad’s moment method for Boltzmann equation. We focus on the hyperbolicity of the reduced model, which is essential for the existence of its classical solution as a Cauchy problem. The theory of the framework we developed in the past years is then introduced, which preserves the hyperbolic nature of the kinetic equations with high universality. Some lastest progress on the comparison between models with/without hyperbolicity is presented to validate the hyperbolic moment models for rarefied gases.