A NEW SCHEME FOR MULTIDIMENSIONAL LINE TRANSFER .3. A 2-DIMENSIONAL LAGRANGIAN VARIABLE TENSOR METHOD WITH DISCONTINUOUS FINITE-ELEMENT SN TRANSPORT

We describe a new code-ALTAIR-that has been developed to solve the tim e-dependent non-LTE problem for a multilevel atom in two-dimensional a xisymmetric geometry on a Lagrangian mesh of arbitrary complexity. The method and results are presented here for a two-level atom. The exten sion to a multilevel atom is made by the equivalent two-level atom (ET LA) methods we have recently described in Paper II of this series. The source function of the line formed by the two-level atom is iterated to self-consistency with the radiation held, which is obtained from a system of coupled moment equations that employs an Eddington tensor cl osure using the double-splitting method described in Paper I of this s eries. The Eddington tensor itself is derived from a formal solution o f the photon transport equation, which is based on a new discontinuous finite-element technique; the tensor moment system uses a continuous representation. The Eddington tensor is updated in an outer iteration loop, within which the double-splitting iteration is used to find the self-consistent source function for a given tenser. The resulting meth od shows very rapid convergence of the scattering iteration, even for optically thick regions with scattering albedo near unity. In addition , the spatial structure of the solution is rather insensitive to the s hape of the spatial zones; the calculation of problems with zone aspec t ratios of 1000 to 1 causes no difficulty. Application to several ben chmark calculations, including radiative transfer in a nonorthogonal m esh, is discussed. We find that for two-dimensional problems of astrop hysical interest, many angle rays are required to ensure an accurate s olution.