Non-relativistic limit of the compressible Navier-Stokes-Fourier-P1 approximation model arising in radiation hydrodynamics

TL;DR

This paper rigorously derives the non-relativistic limit of the Navier-Stokes-Fourier-P1 approximation model in radiation hydrodynamics, showing its connection to the general radiation hydrodynamics model under the assumption of a large speed of light.

Contribution

It provides a rigorous mathematical derivation of the non-relativistic limit of the Navier-Stokes-Fourier-P1 model in radiation hydrodynamics, clarifying its relation to the general model.

Findings

Rigorous derivation of the non-relativistic limit.

Validation of the macroscopic model in radiation hydrodynamics.

Clarification of the model's assumptions and approximations.

Abstract

As is well-known that the general radiation hydrodynamics models include two mainly coupled parts: one is macroscopic fluid part, which is governed by the compressible Navier-Stokes-Fourier equations, another is radiation field part, which is described by the transport equation of photons. Under the two physical approximations: "gray" approximation and P1 approximation, one can derive the so-called Navier-Stokes-Fourier-P1 approximation radiation hydrodynamics model from the general one. In this paper we study the non-relativistic limit problem for the Navier-Stokes-Fourier-P1 approximation model due to the fact that the speed of light is much larger than the speed of the macroscopic fluid. Our results give a rigorous derivation of the widely used macroscopic model in radiation hydrodynamics.