Non-relativistic limit of the Euler-HMP$_N$ approximation model arising in radiation hydrodynamics

TL;DR

This paper investigates the non-relativistic limit of a class of computable models in radiation hydrodynamics, combining energy methods and asymptotic analysis to verify the limit for hyperbolic relaxation systems.

Contribution

It establishes the non-relativistic limit of Euler-HMP_N models in radiation hydrodynamics using energy methods and formal asymptotics, confirming their structural stability.

Findings

Models satisfy Yong's structural stability condition

Non-relativistic limit verified through combined energy and asymptotic analysis

Provides a rigorous foundation for the approximation models in radiation hydrodynamics

Abstract

In this paper, we are concerned with the non-relativistic limit of a class of computable approximation models for radiation hydrodynamics. The models consist of the compressible Euler equations coupled with moment closure approximations to the radiative transfer equation. They are first-order partial differential equations with source terms. As hyperbolic relaxation systems, they are showed to satisfy the structural stability condition proposed by W.-A. Yong (1999). Base on this, we verify the non-relativistic limit by combining an energy method with a formal asymptotic analysis.