3D Radiative Transfer on Irregular Grids

Three-dimensional radiative transfer calculations involve extensive amounts of computation. These calculations are done on three-dimensional model atmospheres where the MHD equations are solved. Typically, model atmospheres are run on a discretised Cartesian grid, which is often not ideal for detailed calculation of spectral lines. This thesis investigates radiative transfer on irregular grids to improve spectral line calculations. In one-dimensional radiative transfer, optimised grids lead to an accelerated convergence in solving the radiative transfer equation iteratively. These optimised grids are partitioned unevenly, and extending such grids to three dimensions requires different ray tracing methods than the traditional long and short characteristics. In this thesis, I develop a ray tracing algorithm on irregular grids. I construct a Voronoi diagram on the irregular grid and trace rays along its Delaunay lines. This ray tracing method gives good results in the searchlight beam test, producing similar amounts of diffusion as the short characteristics method with a piecewise linear interpolation. The irregular grid framework is extended to a two-level atom problem in a quiet Sun MHD simulation. On a reduced resolution of the atmospheric model, the quality of synthesised spectra calculated with irregular grids is not as good as that of the Cartesian grid. However, optimised irregular grids converge nearly twice as fast as regular Cartesian grids. Although these calculations are modest with grid points, I also expect an accelerated convergence for higher resolution calculations. This work establishes irregular grids' capability to calculate three-dimensional radiative transfer in the solar atmosphere. Further improvement to the methods can make NLTE calculations on irregular grids more fitting than on Cartesian grids