Extending a Hybrid Godunov Method for Radiation Hydrodynamics to Multiple Dimensions

TL;DR

This paper extends a one-dimensional hybrid Godunov method for radiation hydrodynamics to three dimensions, providing detailed algorithms for multidimensional implementation, with future work to demonstrate its robustness through numerical tests.

Contribution

It introduces a multidimensional extension of an existing one-dimensional radiation hydrodynamics method, maintaining asymptotic limits and stability properties.

Findings

Algorithmic framework for 3D radiation hydrodynamics

Preserves asymptotic limits across regimes

Ensures stability from free streaming to diffusion

Abstract

This paper presents a hybrid Godunov method for three-dimensional radiation hydrodynamics. The multidimensional technique outlined in this paper is an extension of the one-dimensional method that was developed by Sekora & Stone 2009, 2010. The earlier one-dimensional technique was shown to preserve certain asymptotic limits and be 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. This paper gives the algorithmic details for constructing a multidimensional method. A future paper will present numerical tests that demonstrate the robustness of the computational technique across a wide-range of parameter space.