High-order gas-kinetic scheme for radiation hydrodynamics in equilibrium-diffusion limit

TL;DR

This paper introduces a high-order gas-kinetic scheme for radiation hydrodynamics in the equilibrium-diffusion limit, combining implicit-explicit time integration with advanced spatial reconstruction to improve accuracy and efficiency.

Contribution

It develops a novel high-order gas-kinetic scheme using IMEX and WENO methods for radiation hydrodynamics in the equilibrium-diffusion limit, addressing time scale disparities.

Findings

The scheme achieves high-order accuracy in both space and time.

It demonstrates robustness across various numerical tests.

The implicit-explicit approach effectively handles different time scales.

Abstract

In this paper, a high-order gas-kinetic scheme is developed for the equation of radiation hydrodynamics in equilibrium-diffusion limit which describes the interaction between matter and radiation. To recover RHE, the Bhatnagar-Gross-Krook (BGK) model with modified equilibrium state is considered. In the equilibrium-diffusion limit, the time scales of radiation diffusion and hydrodynamic part are different, and it will make the time step very small for the fully explicit scheme. An implicit-explicit (IMEX) scheme is applied, in which the hydrodynamic part is treated explicitly and the radiation diffusion is treated implicitly. For the hydrodynamics part, a time dependent gas distribution function can be constructed by the integral solution of modified BGK equation, and the time dependent numerical fluxes can be obtained by taking moments of gas distribution function. For the radiation diffusion term, the nonlinear generalized minimal residual (GMRES) method is used. To achieve the temporal accuracy, a two-stage method is developed, which is an extension of two-stage method for hyperbolic conservation law. For the spatial accuracy, the multidimensional weighted essential non-oscillation (WENO) scheme is used for the spatial reconstruction. A variety of numerical tests are provided for the performance of current scheme, including the order of accuracy and robustness.