# General Relativity (GR)

Working on Schwartzchild solution to Einsteins field equation and how to work with Schwartzchild coordinate and metric. GR this week took most of Monday and all of Thursday. We have an exam next week so I likely won’t get much else done.

# HLLD Solver

I finished writing the HLLD solver, the tester for it, and the visualization script. Debugging still needs to be done and that will be my ongoing work. I have a GR exam next week though so I’ll likely be busy with that.

Actually implementing the HLLD solver turned out to be significantly more complex than anticipated. I originally thought it would be a simple extension of the HLLC solver but that was not the case. The L and R states were similar, just a slightly different form of the flux equation. The star state was significantly more complicated to implement and was made much more complicated by the needs of the double star state. The double star state requires the entire star state and star flux from one side as expected but it also requires the velocity and magnetic field vectors from the other sides star state. Splitting out the calculations for velocity and magnetic field into their own function partly solved that issue. The other major complicating factor was that in different spots in the algorithm you explicitly need the left or right star state and in other spots you just need to state for whichever side you’re on. Making sure the logic worked for all of these constraints made the implementation significantly more complex than the implementation of the HLLC Riemann solver.

## Useful links

Original HLLD paper: Miyoshi & Kusano 2005

Blog post on the HLLD Algorithm: HLLD Algorithm

Original VL+CT paper: Stone & Gardiner 2009