2006/11/30 by Mark R. Krumholz, Richard Klein, Richard I. Klein +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Algorithm #Applied mathematics #Code (set theory) #Computational Fluid Dynamics and Aerodynamics #Computer science #Diffusion #Fluid Dynamics and Turbulent Flows #Flux (metallurgy) #Frame (networking) #Geometry #Mathematics #Optics #Physics #Polygon mesh #Radiation #Radiation transport #Range (aeronautics) #Set (abstract data type) #Statistical physics #astro-ph
paper · pdf · doi:10.1086/520791
19 pages, 12 figures, emulateapj format, accepted to ApJS. This version contains additional code verification tests and some changes to the discussion. The basic results derived are unchanged
arxiv created 2007/05/28 · openalex publication_date 2007/09/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We analyze the mixed frame equations of radiation hydrodynamics under the approximations of flux-limited diffusion and a thermal radiation field, and derive the minimal set of evolution equations that includes all terms that are of leading order in any regime of non-relativistic radiation hydrodynamics. Our equations are accurate to first order in v/c in the static diffusion regime. In contrast, we show that previous lower order derivations of these equations omit leading terms in at least some regimes. In comparison to comoving frame formulations of radiation hydrodynamics, our equations have the advantage that they manifestly conserve total energy, making them very well-suited to numerical simulations, particularly with adaptive meshes. For systems in the static diffusion regime, our analysis also suggests an algorithm that is both simpler and faster than earlier comoving frame methods. We implement this algorithm in the Orion adaptive mesh refinement code, and show that it performs well in a range of test problems.