Monte Carlo discretization of general relativistic radiation transport

TL;DR

This paper introduces a hybrid Monte Carlo discretization method for general relativistic radiation transport, enabling efficient, parallelizable simulations that handle both optically thick and thin regions with adaptive capabilities.

Contribution

It presents a novel discretization scheme based on surface flux estimators, suitable for numerical implementation in complex relativistic radiation transport problems.

Findings

Handles optically thick regions with formal solutions within cells

Designed for parallel computing environments

Supports adaptive techniques with unspecified probability densities

Abstract

An indirect, hybrid Monte Carlo discretization of general relativistic kinetic theory suitable for the development of numerical schemes for radiation transport is presented. The discretization is based on surface flux estimators obtained from a local decomposition of the distribution function, and can handle optically thick regions by means of formal solutions within each cell. Furthermore, the scheme is designed for parallel implementation, and it admits the use of adaptive techniques by virtue of leaving all probability density functions unspecified. Some considerations for numerical uses of the scheme are discussed.