Space-time domain velocity distributions in isotropic radiative transfer in two dimensions

TL;DR

This paper derives exact analytical solutions for the radiative transfer equation in two dimensions with isotropic scattering, providing detailed space-time distributions of intensity and radiance, and validates them against Monte-Carlo simulations.

Contribution

It presents the first exact solutions for 2D isotropic radiative transfer in space-time, enhancing understanding and validation of numerical methods.

Findings

Exact solutions for 2D isotropic radiative transfer obtained.

Analytical results validated with Monte-Carlo simulations.

Provides detailed space-time distributions of intensity and radiance.

Abstract

We compute the exact solutions of the radiative transfer equation in two dimensions for isotropic scattering. The intensity and the radiance are given in the space-time domain for isotropic and unidirectional sources. These analytical results are compared to Monte-Carlo simulations in four particular situations.