Improved moving-puncture techniques for compact binary simulations

To fully unlock the scientific potential of upcoming gravitational wave (GW) interferometers, numerical relativity (NR) simulation accuracy will need to be greatly enhanced. We present three infrastructure-agnostic improvements to the moving-puncture approach for binary black hole (BBH) simulations, aimed at greatly 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 adaptive mesh refinement framework. Our improvements include a modified Kreiss-Oliger dissipation prescription, a Hamiltonian constraint damping adjustment to the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) equations, and an extra term to the $1+\mathrm{log}$ 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 greatly reduce GW noise, enabling the extraction of high-order GW modes previously obscured by numerical noise. They also improve convergence properties near and inside the convergent regime, reduce Hamiltonian (momentum) constraint violations in the strong-field region by roughly 2 (3) orders of magnitude, and in the GW-extraction zone by 5 (2) 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.