Using 3D Voronoi grids in radiative transfer simulations

Abstract

Context. Probing the structure of complex astrophysical objects requires effective three-dimensional (3D) numerical simulation of the relevant radiative transfer (RT) processes. As with any numerical simulation code, the choice of an appropriate discretization is crucial. Adaptive grids with cuboidal cells such as octrees have proven very popular; however, several recently introduced hydrodynamical and RT codes are based on a Voronoi tessellation of the spatial domain. An unstructured grid of this nature poses new challenges in laying down the rays (straight paths) needed in RT codes. Aims. We show that it is straightforward to implement accurate and efficient RT on 3D Voronoi grids. Methods. We present a method for computing straight paths between two arbitrary points through a 3D Voronoi grid in the context of a RT code. We implement this grid in our RT code SKIRT, using the open source library Voro++ to obtain the relevant properties of the Voronoi grid cells based solely on the generating points. We compare the results obtained through the Voronoi grid with those generated by an octree grid for two synthetic models, and we perform the well-known Pascucci RT benchmark using the Voronoi grid. Results. The presented algorithm produces correct results for our test models. Shooting photon packages through the geometrically much more complex 3D Voronoi grid is only about three times slower than the equivalent process in an octree grid with the same number of cells, while in fact the total number of Voronoi grid cells may be lower for an equally good representation of the density field. Conclusions. The benefits of using a Voronoi grid in RT simulation codes will often outweigh the somewhat slower performance.

Hierarchical octree andk-d tree grids for 3D radiative transfer simulations

“…These grids have existed for a long time, but they have recently gained increases popularity thanks to the development of hydrodynamics codes that operate on them (Xu 1997;Springel 2010;Duffell & MacFadyen 2011). Radiative transfer on such grids has been shown to be possible (Paardekooper et al 2010;Brinch & Hogerheijde 2010;Camps et al 2013). While unstructured grids can probably not compete with hierarchical grids in terms of grid traversal, they could be more efficient in some situations, e.g.…”

Insights from Synthetic Star-forming Regions. I. Reliable Mock Observations from SPH Simulations

“…Voronoi Sites Choosing the Voronoi sites of the tessellation wisely is one of the critical elements when setting up a Voronoi mesh efficiently. While a rule of thumb is that regions with higher densities should have higher resolution and hence more sites, one has to keep in mind that very optically thick regions will trap photons and many such cells are not beneficial to the radiative transfer calculation (for a discussion of this, see Camps et al 2013). In Figure 4, we plot density slices of different site distributions within a box of 1 pc and highlight accreting sink particles in red and sink particles in the ionizing bubble in blue.…”

High-resolution, 3D radiative transfer modeling

“…SKIRT can furthermore be applied to model the emission of simulated galaxies from hydrodynamical simulations (Camps et al 2013a). An important extension of SKIRT in view of high-resolution radiative transfer models involves the implementation of adaptive grid structures such as the hierarchical Octree (Kurosawa & Hillier 2001;Niccolini & Alcolea 2006), k-d grid structures, and Voronoi tesselations (Voronoi 1908), which are described in more detail in Saftly et al (2013Saftly et al ( , 2014 and Camps et al (2013b), respectively. Such adaptive grid structures allow to increase the resolution in the dust grid where dust clumps or asymmetric spiral arm structures are present, and at the same time keep the computational cost limited.…”