  To fully unlock the scientific potential of upcoming gravitational wave (GW)
interferometers, numerical relativity (NR) simulation accuracy must be greatly
enhanced. We present three infrastructure-agnostic improvements to the
moving-puncture approach for binary black hole (BBH) simulations, aimed at
significantly reducing constraint violation and improving GW predictions.
Although these improvements were developed within the highly efficient NR code
BlackHoles@Home, we demonstrate their effectiveness in the widely adopted
Einstein Toolkit/Carpet AMR framework. Our improvements include a modified
Kreiss-Oliger dissipation prescription, a Hamiltonian-constraint-damping
adjustment to the BSSN equations, and an additional term to the 1+log lapse
evolution equation that slows the development of the sharp lapse feature, which
dominates numerical errors in BBH simulations. With minimal increase in
computational cost, these improvements significantly reduce GW noise, enabling
the extraction of high-order GW modes previously obscured by numerical noise.
They also improve convergence properties, reduce Hamiltonian (momentum)
constraint violations in the strong-field region by approximately two (three)
orders of magnitude, and in the GW-extraction zone by five (two) orders of
magnitude. To promote community adoption, we have open-sourced the improved
Einstein Toolkit thorn BaikalVacuum used in this work. Although our focus is on
BBH evolutions and the BSSN formulation, these improvements may also benefit
compact binary simulations involving matter and other formulations, a focus for
future investigations.
