Numerical methods for multidimensional radiative transfer - Meinköhn, Erik; Kanschat, Guido; Rannacher, Rolf; Wehrse, Rainer (Reactive flows, diffusion and transport, 2007)
This paper presents a finite element method for solving the resonance line transfer problem in moving media. The algorithm is capable of dealing with three spatial dimensions, using hierarchically structured grids which are locally refined by means of duality-based a posteriori error estimates. Application of the method to coherent isotropic scattering and complete redistribution gives a result of matrix structure which is discussed in the paper. The solution is obtained by way of an iterative procedure, which solves a succession of quasi-monochromatic radiative transfer problems. It is therefore immediately evident that any simulation of the extended frequency-dependent model requires a solution strategy for the elementary monochromatic transfer problem, which is fast as well as accurate. The present implementation is applicable to arbitrary model configurations with optical depths up to 103-104. Additionally, a combination of a discontinuous finite element method with a superior preconditioning method is presented, which is designed to overcome the extremely poor convergence properties of the linear solver for optically thick and highly scattering media. The contents of this article is as follows: Introduction Overview: numerical methods Monochromatic 3D radiative transfer Polychromatic 3D line transfer Test calculations Applications Multi-model preconditioning Conclusion