The system of ionized gas dynamics

TL;DR

This paper analyzes a complex system of equations governing high-temperature ionized gas dynamics in one dimension, revealing geometric properties, loss of convexity, and shock wave structures, with implications for shock tube problem studies.

Contribution

It characterizes the geometric and nonlinear properties of the ionized gas system, including loss of convexity and shock wave structure analysis, under thermodynamic equilibrium.

Findings

Loss of convexity in characteristic fields

Loss of entropy concavity in a bounded region

Detailed analysis of shock wave structures

Abstract

The aim of this paper is to study a system of three equations for ionized gas dynamics at high temperature, in one spatial dimension. In addition to the mass density, pressure and particle velocity, a further quantity is needed, namely, the degree of ionization. The system is supplemented by the first and second law of thermodynamics and by an equation of state; all of them involve the degree of ionization. At last, under the assumption of thermal equilibrium, the system is closed by requiring Saha's ionization equation. The geometric properties of the system are rather complicated: in particular, we prove the loss of convexity (genuine nonlinearity) for both forward and backward characteristic fields, and hence the loss of concavity of the physical entropy. This takes place in a small bounded region, which we are able to characterize by numerical estimates on the state functions. The structure of shock waves is also studied by a detailed analysis of the Hugoniot locus, which will be used in a forthcoming paper to study the shock tube problem.