MODA: a new algorithm to compute optical depths in multi-dimensional hydrodynamic simulations

We introduce a new algorithm for the calculation of multidimensional optical depths in approximate radiative transport schemes, equally applicable to neutrinos and photons. Motivated by (but not limited to) neutrino transport in three-dimensional simulations of core-collapse supernovae and neutron star mergers, our method makes no assumptions about the geometry of the matter distribution, apart from expecting optically transparent boundaries. Based on local information about opacities, the algorithm figures out an escape route that tends to minimize the optical depth without assuming any pre-defined paths for radiation. Its adaptivity makes it suitable for a variety of astrophysical settings with complicated geometry (e.g., core-collapse supernovae, compact binary mergers, tidal disruptions, star formation, etc.). We implement the MODA algorithm into both a Eulerian hydrodynamics code with a fixed, uniform grid and into an SPH code where we make use a tree structure that is otherwise used for searching neighbours and calculating gravity. In a series of numerical experiments, we compare the MODA results with analytically known solutions. We also use snapshots from actual 3D simulations and compare the results of MODA with those obtained with other methods such as the global and local ray-by-ray method. It turns out that MODA achieves excellent accuracy at a moderate computational cost. In an appendix we also discuss implementation details and parallelization strategies.