Numerical Tests and Properties of Waves in Radiating Fluids

TL;DR

This paper analyzes an analytical wave solution in radiating fluids to serve as a test for radiation hydrodynamics codes, highlighting implementation challenges and the non-causality issue of flux-limited diffusion.

Contribution

It provides detailed insights into the properties of wave solutions in radiating fluids and evaluates their numerical implementation, emphasizing the limitations of flux-limited diffusion.

Findings

Analytical solutions describe radiative acoustic and diffusion waves.

Implementation requires careful handling of wave features.

Flux-limited diffusion does not preserve causality.

Abstract

We discuss the properties of an analytical solution for waves in radiating fluids, with a view towards its implementation as a quantitative test of radiation hydrodynamics codes. A homogeneous radiating fluid in local thermodynamic equilibrium is periodically driven at the boundary of a one-dimensional domain, and the solution describes the propagation of the waves thus excited. Two modes are excited for a given driving frequency, generally referred to as a radiative acoustic wave and a radiative diffusion wave. While the analytical solution is well known, several features are highlighted here that require care during its numerical implementation. We compare the solution in a wide range of parameter space to a numerical integration with a Lagrangian radiation hydrodynamics code. Our most significant observation is that flux-limited diffusion does not preserve causality for waves on a homogeneous background.