ARGOT: Accelerated radiative transfer on grids using oct-tree

TL;DR

This paper introduces two efficient numerical methods using oct-tree structures to accelerate 3D radiative transfer calculations around point sources, improving computational speed while maintaining accuracy.

Contribution

It presents novel prescriptions for grouping distant sources and solving radiative transfer on supermeshes or as point sources, enhancing efficiency in grid-based simulations.

Findings

Computational time scales as N_m log(N_m) log(N_s) with the supermesh method.

The point source approximation yields better results with slightly higher computational cost.

Methods are compatible with adaptive mesh refinement and easy to implement.

Abstract

We present two types of numerical prescriptions that accelerate the radiative transfer calculation around point sources within a three-dimensional Cartesian grid by using the oct-tree structure for the distribution of radiation sources. In one prescription, distant radiation sources are grouped as a bright extended source when the group's angular size, $\theta_{\rm s}$, is smaller than a critical value, $\theta_{\rm crit}$, and radiative transfer is solved on supermeshes whose angular sizes are similar to that of the group of sources. The supermesh structure is constructed by coarse-graining the mesh structure. With this method, the computational time scales with $N_{\rm m} \log(N_{\rm m}) \log(N_{\rm s})$ where $N_{\rm m}$ and $N_{\rm s}$ are the number of meshes and that of radiation sources, respectively. While this method is very efficient, it inevitably overestimates the optical depth when a group of sources acts as an extended powerful radiation source and affects distant meshes. In the other prescription, a distant group of sources is treated as a bright point source ignoring the spatial extent of the group and the radiative transfer is solved on the meshes rather than the supermeshes. This prescription is simply a grid-based version of {\scriptsize START} by Hasegawa & Umemura and yields better results in general with slightly more computational cost ($\propto N_{\rm m}^{4/3} \log(N_{\rm s})$) than the supermesh prescription. Our methods can easily be implemented to any grid-based hydrodynamic codes and are well-suited to the adaptive mesh refinement methods.