On the Solution of the Time-Dependent inertial-Frame Equation of radiative Transfer in Moving Media to [formula omitted]

Abstract

A stable and efficient mixed-frame method has been formulated for the solution of the time-dependent equation of radiative transfer with full retention of all velocity dependent terms to O( v c) . The method retains the simplicity of the differential operator found in the inertial frame while transforming the absorption and emission coefficients to the comoving frame keeping them isotropic. The method is ideally suited to continuum calculations. To correctly treat the time dependence of the radiation field over fluid-flow time increments, the velocity-dependent terms on the right-hand side of both the transfer and moment equations must be retained for consistency. Both explicit and two- and three-level implicit schemes have been explored for a variety of time-dependent problems and it has been concluded that an implicit-backward Euler scheme works best for propagating a radiation front, but that these schemes are essentially first-order accurate in the space derivative. A second order scheme was formulated with the method of lines which should provide higher spatial accuracy. The formulation naturally couples to hydrodynamics in both the Eulerian and Lagrangian formulations for application to astrophysical flows. It is shown that for uniform flow between the fixed and comoving frames, the solution of the Lorentz transformation of the integrated moments provides a powerful check on the formulation and solution.