Asymptotic constraints for 1D planar grey photon diffusion from linear transport with special-relativistic effects

TL;DR

This paper derives a relativistic grey photon diffusion equation in 1D planar geometry using asymptotic analysis, avoiding non-physical assumptions and allowing continuous photon directions, with preliminary numerical validation.

Contribution

It introduces a novel asymptotic derivation of a relativistic diffusion equation in the lab frame that accounts for special-relativistic effects without restrictive velocity assumptions.

Findings

Derived a drift-diffusion equation for photons in the lab frame

Equation reduces to advection at relativistic speeds

Preliminary numerical experiments show good agreement with Monte Carlo simulations

Abstract

We derive a grey linear diffusion equation for photons with respect to inertial (or lab-frame) space and time, using asymptotic analysis in 1D planar geometry. The solution of the equation is the comoving radiation energy density. Our analysis does not make use of assumptions about the magnitude of velocity; instead we derive an asymptotic scaling in the lab frame such that we avoid apparent non-physical pathologies that are encountered with the standard static-matter scaling. We permit the photon direction to be continuous (as opposed to constraining the analysis to discrete ordinates). The result is a drift-diffusion equation in the lab frame for comoving radiation energy density, with an adiabatic term that matches the standard semi-relativistic diffusion equation. Following a recent study for discrete directions, this equation reduces to a pure advection equation as the velocity approaches the speed of light. We perform preliminary numerical experiments comparing solutions to relativistic lab-frame Monte Carlo transport and to the well-known semi-relativistic diffusion equation.