  We describe the implementation of sophisticated numerical techniques for
general-relativistic magnetohydrodynamics simulations in the Athena++ code
framework. Improvements over many existing codes include the use of advanced
Riemann solvers and of staggered-mesh constrained transport. Combined with
considerations for computational performance and parallel scalability, these
allow us to investigate black hole accretion flows with unprecedented accuracy.
The capability of the code is demonstrated by exploring magnetically arrested
disks.
