控制约束违反的调整BSSN系统的数值试验
Numerical experiments of adjusted BSSN systems for controlling constraint violations
摘要：
我们提出了我们的数值比较广泛使用的BSSN制定的数值相对论的今天，其调整后的版本使用的限制。我们进行了三个测试平台：规范波，线性波，和高迪波测试，提出了墨西哥研讨会上的制定问题的爱因斯坦方程。我们尝试了三种调整，这是以前提出的约束传播方程的分析，并研究它们如何提高进化的精度和稳定性。我们观察到，所提出的拉格朗日乘子的签名总是正确的，并且调整提高了模拟的收敛性和稳定性。当原始BSSN系统已经显示出令人满意的良好演进时（例如，线性波测试），调整后的版本也与那些演变一致;而在某些情况下（例如，规范波或Gowdy波测试），使用调整后的系统的模拟持续时间是使用原始BSSN方程的10倍。我们的演示意味着一个潜在的构建一个强大的进化系统，即使在高度动态的情况下，对违反约束。
英文摘要：
We present our numerical comparisons between the BSSN formulation widely used in numerical relativity today and its adjusted versions using constraints. We performed three testbeds: gauge-wave, linear wave, and Gowdy-wave tests, proposed by the Mexico workshop on the formulation problem of the Einstein equations. We tried three kinds of adjustments, which were previously proposed from the analysis of the constraint propagation equations, and investigated how they improve the accuracy and stability of evolutions. We observed that the signature of the proposed Lagrange multipliers are always right and the adjustments improve the convergence and stability of the simulations. When the original BSSN system already shows satisfactory good evolutions (e.g., linear wave test), the adjusted versions also coincide with those evolutions; while in some cases (e.g., gauge-wave or Gowdy-wave tests) the simulations using the adjusted systems last 10 times as long as those using the original BSSN equations. Our demonstrations imply a potential to construct a robust evolution system against constraint violations even in highly dynamical situations.
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