A new scheme for multidimensional line transfer .3. A two-dimensional Lagrangian variable tensor method with discontinuous finite-element Sn transport

We describe a new code-ALTAIR-that has been developed to solve the time-dependent non-LTE problem for a multilevel atom in two-dimensional axisymmetric geometry on a Lagrangian mesh of arbitrary complexity. The method and results are presented here for a two-level atom. The extension to a multilevel atom is made by the equivalent two-level atom (ETLA) 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 closure using the double-splitting method described in Paper I of this series. The Eddington tensor itself is derived from a formal solution of 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 method 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 shape of the spatial zones; the calculation of problems with zone aspect ratios of 1000 to 1 causes no difficulty. Application to several benchmark calculations, including radiative transfer in a nonorthogonal mesh, is discussed. We find that for two-dimensional problems of astrophysical interest, many angle rays are required to ensure an accurate solution.