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 $1+\log$ 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.

中文翻译：

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改进的紧凑二进制模拟的移动穿刺技术


为了充分释放即将推出的引力波（GW）干涉仪的科学潜力，需要大大提高数值相对论（NR）模拟的精度。我们对二元黑洞（BBH）模拟的移动穿刺方法提出了三种与基础设施无关的改进，旨在大大减少约束违规并改进引力波预测。尽管这些改进是在高效的 NR 代码brakholes @ home中开发的，但我们在广泛采用的einstein工具包/地毯自适应网格细化框架中证明了它们的有效性。我们的改进包括修改的 Kreiss-Oliger 耗散处方、对 Baumgarte-Shapiro-Shibata-Nakamura (BSSN) 方程的哈密顿约束阻尼调整以及对 $1+\log$ 延时演化方程减缓了急剧延时特征的发展，该特征在 BBH 模拟中占主导地位。在计算成本增加最小的情况下，这些改进大大降低了引力波噪声，从而能够提取以前被数值噪声掩盖的高阶引力波模式。它们还改善了收敛区域附近和内部的收敛特性，将强场区域中的哈密顿（动量）约束违规减少了大约 2 (3) 个数量级，将引力波提取区域中的哈密顿（动量）约束违规减少了 5 (2) 个数量级。为了促进社区采用，我们开源了本工作中使用的改进的爱因斯坦工具包thorn b aikal v acuum。 尽管我们的重点是 BBH 演化和 BSSN 公式，但这些改进也可能有利于涉及物质和其他公式的紧凑二元模拟，这是未来研究的重点。