On Hyperbolicity of 13-Moment System

TL;DR

This paper analyzes the hyperbolicity of Grad's 13-moment system, identifies issues with the original system's equilibrium point, and proposes a modified system with an expanded phase density that ensures equilibrium lies within the hyperbolicity region.

Contribution

The authors introduce a compact expansion of phase density leading to a modified 13-moment system with improved hyperbolicity properties.

Findings

Original system's equilibrium is outside the hyperbolicity region.

Modified system's equilibrium is inside the hyperbolicity region.

A concise criterion for hyperbolicity is derived.

Abstract

We point out that the thermodynamic equilibrium is not an interior point of the hyperbolicity region of Grad's 13-moment system. With a compact expansion of the phase density, which is compacter than Grad's expansion, we derived a modified 13-moment system. The new 13-moment system admits the thermodynamic equilibrium as an interior point of its hyperbolicity region. We deduce a concise criterion to ensure the hyperbolicity, thus the hyperbolicity region can be quantitatively depicted.