Einstein方程的外边界处理
Testing outer boundary treatments for the Einstein equations
摘要：
用一个简单的测试问题：一个Schwarzschild黑洞与传出的引力波扰动的处理外边界的数值相对论的各种方法进行了比较。使用不同的边界处理计算的数值解进行比较，以获得一个“参考”的数值解放置在一个非常大的半径外边界。对于每个边界处理，将包括约束违反和提取的引力波的完整解与参考解进行比较，从而评估由人工边界引起的反射。这些测试使用爱因斯坦方程的一阶广义调和公式。对该系统的约束保持边界条件进行了评述，提出了一种改进的规范自由度边界条件。这里评估的替代边界条件包括冻结传入的特征场，Sommerfeld边界条件，以及Kreiss和Winicour的约束保持边界条件。而不同的方法来处理边界，如海绵层和空间紧凑化，也进行了测试。总的来说，这里找到的最佳处理方法结合了保留约束、冻结Newman-Penrose标量Psi_0和控制规范反射的边界条件。
英文摘要：
Various methods of treating outer boundaries in numerical relativity are compared using a simple test problem: a Schwarzschild black hole with an outgoing gravitational wave perturbation. Numerical solutions computed using different boundary treatments are compared to a `reference' numerical solution obtained by placing the outer boundary at a very large radius. For each boundary treatment, the full solutions including constraint violations and extracted gravitational waves are compared to those of the reference solution, thereby assessing the reflections caused by the artificial boundary. These tests use a first-order generalized harmonic formulation of the Einstein equations. Constraint-preserving boundary conditions for this system are reviewed, and an improved boundary condition on the gauge degrees of freedom is presented. Alternate boundary conditions evaluated here include freezing the incoming characteristic fields, Sommerfeld boundary conditions, and the constraint-preserving boundary conditions of Kreiss and Winicour. Rather different approaches to boundary treatments, such as sponge layers and spatial compactification, are also tested. Overall the best treatment found here combines boundary conditions that preserve the constraints, freeze the Newman-Penrose scalar Psi_0, and control gauge reflections.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
