Discrete-Ordinates Methods for Radiative Transfer in the Non-Relativistic Stellar Regime

Jim Morel
Los Alamos National Laboratory

We give an overview of discrete-ordinates or SN methods for radiative transfer in the nonrelativistic
stellar regime. We ?rst describe the basic equations of radiative transfer, which
consist of a transfer equation for the angular intensity and a material temperature equation.
The transfer equation considers emission, absorption, and Thompson scattering. If required,
Compton scattering is separately treated via operator splitting. The material temperature
equation includes absorption and emission terms. If required, heat conduction is treated
via operator splitting. A Newton-like method is used to solve the nonlinear equations. The
associated linearization procedure enables the material temperature to be eliminated from
the transfer equation. We next describe discretization and solution techniques for the linearized
transfer equation. The SN method is generally refers to an angular discretization
of the transfer equation that is based upon collocation at a discrete set of directions that
also serve as quadrature points for evaluating directional integrals. Temporal discretization
techniques include the traditional backward-Euler and Crank-Nicholson methods. For illustative
purposes, we assume the backward-Euler method. The standard multigroup method is
almost exclusively used for energy or frequency discretization. Spatial discretization requires
considerable care and is almost always based upon some type of discontinuous method. The
rather severe requirements placed upon spatial discretization schemes are discussed and an
example of a good 1-D scheme is given. The basic source iteration technique for solving the
transfer equation is described next, followed by a description of two traditional di?usionbased
techniques for accelerating the convergence of the source iterations. We next discuss
the application of Krylov methods to the solution of the transfer equation, and the recasting
of traditional acceleration techniques as preconditioners. Finally, we discuss a simpli?ed nonrelativistic
model for material-motion corrections to the Eulerian-frame transfer equation for
use in radiation-hydrodynamics calculations.

Presentation (PDF File)

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