Radiative processes can be very important in astrophysical flows. At the same time however, it can be quite tricky to implement radiation transport in a hydrodynamical code. In an attempt to help make it easier to understand how to incorporate radiation into your code (or how the current implementation in your code works), I’ve put together a short handbook that covers the basics of implementing a radiation module in the flux-limited diffusion approximation. It might not be the most state-of-the-art method, but it’s definitely sufficient for most cases (and by far better than a simple thermal relaxation approach).
This handbook will walk you through the set of equations that you will need to solve, along with how to discretize, arrange, and solve the problem with efficient numerical techniques. It also covers the basics of how to handle heating from the central star accurately, by ray-tracing starlight from the star onto the disk. Combined, the coupled radiation-irradiation equations set the temperature profile for a passive, irradiated disk.
Topics covered:
- Discretization of the radiation-energy coupled equations
- Implicit formalism and matrix form of the problem
- Boundary conditions
- Numerical solvers and preconditioning
- Discretization of the stellar irradiation term
- Radiation-irradiation coupling
- Frequency-dependent irradiation
⚠️ This document does not cover how to derive the equations themselves, or how one arrives at the flux-limited diffusion closure. For more information on the topic, you should definitely check out Kees Dullemond’s lecture on radiative transfer.
If this handbook has helped you implement radiation transport in your code, you might also want to test that your implementation behaves as expected. You can find a good test problem in the Appendix of this paper, which you can use to verify that your module works!
Download the handbook here (PDF), or use the embedded viewer below: