A Higher Order Godunov Method for Radiation Hydrodynamics: Radiation Subsystem

TL;DR

This paper introduces a second-order Godunov method for radiation hydrodynamics that effectively couples stiff source terms with hyperbolic conservation laws, ensuring accuracy and stability across different physical regimes.

Contribution

The paper presents a novel higher order Godunov method that directly couples stiff source effects with hyperbolic structures in radiation hydrodynamics, improving accuracy and stability.

Findings

Achieves second order accuracy in time and space.

Remains stable and accurate across multiple physical regimes.

Numerical tests confirm second order convergence.

Abstract

A higher order Godunov method for the radiation subsystem of radiation hydrodynamics is presented. A key ingredient of the method is the direct coupling of stiff source term effects to the hyperbolic structure of the system of conservation laws; it is composed of a predictor step that is based on Duhamel's principle and a corrector step that is based on Picard iteration. The method is second order accurate in both time and space, unsplit, asymptotically preserving, and uniformly well behaved from the photon free streaming (hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and to the strong equilibrium diffusion (hyperbolic) limit. Numerical tests demonstrate second order convergence across various parameter regimes.