I have recently been working on software which uses ray tracing/marching to render a black hole in the Schwarzchild metric. I've implemented most everything that I originally set out to do, and I am currently working to implement Kerr black holes as well.
See progress photos/video here.
While I'm very pleased that almost everything is directly computed from physical principles, my model of the accretion disk is still largely guesstimated. I'm using temperature curves derived in these lecture notes to determine blackbody coloration, and calculating doppler shift and beaming using the velocity of a circular orbit at that radius, but that's about where the physical principles end.
Currently I'm rendering the gas of the accretion disk by doing a volumetric render, ray marching through a noise texture. Then I add a bit of a spiral to the noise texture, shifting the azimuth coordinate linearly with the radial coordinate. Finally, and this is what really keeps me up at night, I simply rotate the entire disk linearly in time. This is not at all in accordance with the calculated velocity, but if I naively put an r^(-3/2) angular speed, then the noise texture smears out, losing the nice bands of coherence and creating more like rings.
So what I'm wondering is, could anyone with knowledge in relativity/astrophysics point me in the right direction of how I should be simulating an accretion disk like this? Is there something like density wave theory that would apply in this regime? Should I try and simulate a noisy fluid to achieve a sort of viscosity?
Thanks for any advice!
