On the solution of the time-dependent inertial-frame equation of radiative transfer in moving media to O(v/c)

Astronomy and Astrophysics – Astrophysics

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Astrophysics, Fluid Flow, Inertia, Radiative Transfer, Time Dependence, Atmospheres, Hydrodynamic Equations, Lorentz Transformations, Thomson Scattering, Velocity Distribution

Scientific paper

It is demonstrated that practical schemes can be developed for treating the hybrid time-dependent transfer equation including O(v/c) terms both stably and efficiently, and their coupling into radiation-hydrodynamical calculations is sketched. The mixed-frame equation of transfer and the frequency-dependent and frequency-integrated moment equations are developed. The relative sizes of the terms in the transfer equation and the requirement for keeping all v/c terms in order to obtain exact consistency with the energy equation for the radiating fluid are addressed. The computational approach is discussed in Feautrier variables, including a second-order formulation. Several schemes for the solution method are presented along with test calculations for an unattenuated square wave, attenuated radiation front, irradiated grey atmosphere, and velocity effects in a moving atmosphere. How the transfer equation to O(v/c) can be coupled to the hydrodynamic equations in both an Eulerian and Lagrangian formulation is indicated.

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