Optimized grid for 1D radiative transfer
Background
Three dimensional model atmospheres are typically run on a discretised Cartesian grid, where the MHD equations are solved. This grid is often not ideal for detailed calculation of spectral lines. The naturally-occuring gradients in quantities such as temperature or density can lead to very large steps in optical depth from one grid point to another, leading to numerical errors. There is a large amount of literature on better solvers of the radiative transfer equation for discontinous media (see e.g. Janet et al. 2019, and references therein), but often using higher-order methods also has its drawbacks.
A more basic way of improving the grid of an existing atmosphere model is to simply interpolate the original grid to a finer resolution grid, where any large gradients can be spaced out in a few grid cells. A brute-force approach means just increasing the number of points until all gradients are adequately resolved, but this has the downside of additional computational expense: higher resolution is not needed everywhere, and many points slow down the computation significantly. In iterative non-LTE numerical solvers, this has the added disadvantage that more grid points make the convergence slower. Therefore, it is of great interest to devise an method of optimising an existing grid to the calculation of radiation, speeding up the convergence of non-LTE calculations.
Goal
The goal of this project is to devise an optimal way of improving a 1D stellar atmosphere grid to allow a faster non-LTE calculation of chromospheric lines.
Method
The RH 1.5D code is used to solve the equations of statistical equilibrium for a given model atom and model atmosphere.
Procedure
- Choose a model atom to calculate non-LTE lines formed in the solar chromosphere (e.g. Ca II, Mg II, etc.)
- Using a snapshot from a Bifrost simulation, select a few 1D columns (about 10) to use as 1D atmospheres for this project. You should mix some typical columns, and also several columns with strong gradients where non-LTE calculations take many iterations to converge with the RH 1.5D code. One full Bifrost cube is in /mn/stornext/u3/matsc/rh/Atmos/en024048_hion_385.ncdf
- Build different grid-optimised versions of the 1D atmospheres, e.g. using the following methods:
- Brute force adding many additional points
- Using the same number of points but redistributing them in different ways (e.g. to resolve gradients in temperature, density, or optical depth)
- Using the original grid, but adding a few extra points in the regions with the highest gradients (see point above)
- Run the RH 1.5D code for the chosen atom and different versions of 1D atmospheres. Study the effect on the necessary number of iterations to achieve convergence, total running time, and shape of line profiles. Investigate also with the effect of using different source function interpolations in the formal solver (e.g. linear and cubic hermite), to see if this also changes things.