Kinetic model and numerical method for multispecies radiation hydrodynamic system with multiscale nonequilibrium transport

TL;DR

The paper addresses the challenge of simulating multispecies radiation hydrodynamics across a broad range of optical depths by introducing a kinetic, gray radiative transfer model coupled to a dual-fluid electron–ion system and solving it with an extended Unified Gas-Kinetic Scheme (UGKS). The method unifies transport, diffusion, and energy–momentum exchanges through a three-part operator-splitting algorithm, capturing nonequilibrium dynamics and ensuring correct hydrodynamic and diffusion limits via $I(\boldsymbol{x},\boldsymbol{\Omega},t)$, $E_{\mathcal{R}}$, and $S_{\mathcal{R}}$-driven couplings. The approach is validated with a comprehensive suite of test problems (shock structures, Marshak diffusion, radiative shocks, and 2D Tophat configurations), demonstrating accurate multiscale behavior from free-streaming to diffusion and robust treatment of electron–ion–radiation interactions. The resulting framework offers a computationally efficient, physically faithful tool for studying radiation–plasma phenomena in astrophysics and inertial confinement fusion across diverse energy-density regimes.

Abstract

This paper presents a comprehensive numerical framework for simulating radiation-plasma systems. The radiative transfer process spans multiple flow regimes due to varying fluid opacity across different regions, necessitating a robust numerical approach. We employ the multiscale unified gas-kinetic scheme (UGKS), which accurately captures photon transport phenomena from free streaming to diffusive wave propagation. The UGKS is also applied to the fluid model to address the significant mass disparity between electrons and ions, and their associated transport characteristics in both equilibrium continuum and non-equilibrium rarefied regimes. Our model explicitly incorporates momentum and energy exchanges between radiation and fluid fields in the coupled system, enabling detailed analysis of the complex interactions between electromagnetic and hydrodynamic phenomena. The developed algorithm successfully reproduces both optically thin and optically thick radiation limits while capturing the complex multiscale nonequilibrium dynamics of the coupled system. This unified treatment eliminates the need for separate numerical schemes in different regimes, providing a consistent and computationally effcient approach for the entire domain. The effectiveness and versatility of this approach are demonstrated through extensive numerical validation across a wide range of physical parameters and flow conditions.

Figures (13)

• Figure 1: Shock structure at ${\rm Ma}_\infty = 1.5$. Distributions of (a) number densities and (b) temperatures of electron and ion with the mass ratio $m_\mathcal{E}/m_\mathcal{I} = 0.25$ and number density ratio $n_\mathcal{E}/n_\mathcal{I} = 0.1$. The reference results are from kosuge2001.
• Figure 2: Shock structure at ${\rm Ma}_\infty = 1.5$. Distributions of (a) number densities and (b) temperatures of electron and ion with the mass ratio $m_\mathcal{E}/m_\mathcal{I} = 0.25$ and number density ratio $n_\mathcal{E}/n_\mathcal{I} = 0.9$. The reference results are from kosuge2001.
• Figure 3: Marshak wave case in diffusion limit with $\sigma = 100/T^{3}$, The UGKS solution is compared with the result by solving the diffusion solution sun2015gray.
• Figure 4: Distributions of the radiative shock (a) density, (b) velocity, and (c) temperature with Mach number $\rm{Ma} = 1.5$ and mass ratio $m_\mathcal{E}/m_\mathcal{I} = 1.0$.
• Figure 5: Distributions of the radiative shock (a) density, (b) velocity, and (c) temperature with Mach number $\rm{Ma} = 3.0$ and mass ratio $m_\mathcal{E}/m_\mathcal{I} = 1.0$.