Radiative Transfer

Enzo has two options for radiation transport: an adaptive ray-tracing method, and an implicit flux-limited diffusion solver that is coupled to Enzo’s internal chemistry and cooling solvers. Both are described in more detail below.

Adaptive Ray Tracing

Enzo includes a photon-conserving radiative transfer algorithm that is based on an adaptive ray-tracing method utilizing the HEALPix pixelization of a sphere (Abel & Wandelt 2002). Photons are integrated outward from sources using an adaptive timestepping scheme that preserves accuracy in ionization fronts even in the optically-thin limit. This has been coupled to the chemistry and cooling network to provide ionization and heating rates on a cell-by-cell basis, and has the ability to follow multiple radiation groups, as well as capturing H-minus and H2-photodissociating radiation as well as hydrogen and helium-ionizing radiation. The method is described in detail in Wise & Abel (2011), and a listing of parameters can be found at Radiative Transfer (Ray Tracing) Parameters.

Flux-Limited Diffusion

A second option for radiative transfer is a moment-based method that adds an additional field tracking the radiation energy density. This field is evolved using the flux-limited diffusion method, which transitions smoothly between streaming (optically thin) and opaque limits and is coupled to an ionization network of either purely hydrogen, or both hydrogen and helium. The resulting set of linear equations is solved using the parallel HYPRE framework. Full details on the Enzo implementation of this method can be found in Reynolds et al. (2009), and a listing of parameters can be found at Radiative Transfer (FLD) Parameters.

A Practical Comparison of Methods

Both the adaptive ray-tracing and flux-limited diffusion methods work in both unigrid and adaptive mesh simulations. In general, the adaptive ray-tracing method provides a more accurate solution for point-based radiation sources (i.e., it captures radiation shadowing more accurately), but the computational cost scales roughly with the number of sources. The cost of the flux-limited diffusion solver, on the other hand, has a cost that is independent of the number of sources, which can make it more efficient for large-volume calculations.