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We describe the CRASH (Center for Radiative Shock Hydrodynamics) code, a block adaptive mesh code for multi-material radiation hydrodynamics. The implementation solves the radiation diffusion model with the gray or multigroup method and uses a flux limited diffusion approximation to recover the free-streaming limit. The electrons and ions are allowed to have different temperatures and we include a flux limited electron heat conduction. The radiation hydrodynamic equations are solved in the Eulerian frame by means of a conservative finite volume discretization in either one, two, or three-dimensional slab geometry or in two-dimensional cylindrical symmetry. An operator split method is used to solve these equations in three substeps:(1) solve the hydrodynamic equations with shock-capturing schemes, (2) a linear advection of the radiation in frequency-logarithm space, and (3) an implicit solve of the stiff radiation diffusion, heat conduction, and energy exchange. We present a suite of verification test problems to demonstrate the accuracy and performance of the algorithms. The CRASH code is an extension of the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATS-R-US) code with this new radiation transfer and heat conduction library and equation-of-state and multigroup opacity solvers. Both CRASH and BATS-R-US are part of the publicly available Space Weather Modeling Framework (SWMF).

We present a new spatial discretization method. which enforces conservation on quadrilateral subcells in an arbitrarily connected grid of polygonal cells, for two-dimensional radiative transfer problems. We review what is known about the performance of existing methods for optically thick, diffusive regions of radiative transfer problems, focusing in particular on bilinear discontinuous (BLD) finitezlement methods and the simple cornerhalance (SCB) method. We discuss the close relation of the SCB and BLD methods, and how they differ. By careful analysis, we relate specific properties of the SCB solution to specific approximations in the SCB method. We then build our new method by discarding those SCB approximations that lead to undesirable properties and carefully constructing new approximations designed to yield more desirable properties. We compare BLD, SCB. and the new scheme on a series of test problems in slab and XY geometries; numerical results invariably agree with predictions of the analysis. The new method matches SCB in thick diffusive regions. as it was designed to, but vastly outperforms SCB given cells of fine and intermediate optical thickness, where it achieves results comparable to BLD.

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