We have been working on the Roxane project for a few years. The Roxane project covers a variety of physics in standard geometries of one, two, and three dimensions, including hydrodynamics, volume fraction material advection, material mixing, elastic-plastic strength models, magnetohydrodynamics, 3-T radiation diffusion, detonation shock dynamics, high explosive burn models, etc. Although there are other kinds of AMR used in calculations on structured meshes, we use cell-based AMR.

In this presentation, in addition to AMR, parallel strategy, and IO package, we will particularly describe a numerical approach for solving nonlinear 3-T radiation diffusion equations. For systems of multi-materials with dramatically different material properties, the correct treatment for the discontinuity of material properties is important. We use the governing physics to obtain the effective diffusion coefficient across a material interface for flux calculations on polyhedral meshes. Formulations good for steady states are important even for time-dependent problems for the systems. This often challenges the second order accuracy (in time) of numerical schemes. We applied a rare time-stepping technique to have the both properties. Another important aspect in numerical simulations for 3-T radiation equations is the numerical treatment for interaction between radiation and material. The 3-T radiation diffusion equations are often solved through operator splitting. In our approach radiation and material are fully coupled, and three temperatures are updated simultaneously.