An analytical benchmark for non-equilibrium radiative transfer in an isotropically scattering medium

Benchmark solutions to nontrivial radiation transport problems are crucial to the validation of transport codes, This paper gives an analytical transport solution for non-equilibrium radiative transfer in an infinite and isotropically scattering medium. The radiation source in the medium is isotropic in angle and constant in time (but only exists in a finite period of time), and is allowed to be uniformly distributed in a finite space or to be located at a point. The solution is constructed by applying the Fourier transform with respect to spatial variable and the Laplace transform with respect to temporal variable, The integration over angular variable is treated exactly. The resulting solution, as a function of space and time and in the form of a double integral, is evaluated numerically without much difficulty. Tables and figures are given for the resulting benchmark solution. Published by Elsevier Science Ltd.