I wrote the n-body code for Universe Sandbox ² and I wonder from where you got the impression that we are not using symplectic integration? Especially when you link to my old video which demonstrates a number of symplectic integrators...?

The previous version US1 was really using Semi Implicit Euler, which is symplectic, although not very accurate, and the newer US² uses velocity verlet as the default with support for multiple other higher order schemes. Some symplectic and some not.

As to your comments about the adaptive method, I don't think I have explained in detail what we do now. The description for the 2 year old video was briefly mentioning a method where timestep relates to magnitude of derivative, which is certainly a commonly used method in astrophysics, and I wonder why you would think differently? As to that metric being costly, that is just plain wrong, since the derivative is explicitly calculated anyway. It seems that you are working with fluid dynamics mostly(?) in which case that might explain it. Regardless, that is more or less the go-to method for n-body.

The downside to that method is that it is best suited for pure n-body which is not quite what we have. Especially not with certain new features coming along. Now we use a more generic method where the error is estimated from stepping dt as well as two times ½dt and deriving an error as well as an optimal dt to reach the exact error threshold. Slightly higher cost, but much better suited for generic use. This is also quite standard and something I am sure you know about as well.

I will be happy to discuss this in greater detail, if you want, but for now I just wanted to clear up some apparent misunderstandings.