Testing outer boundary treatments for the Einstein equations
Testing outer boundary treatments for the Einstein equations
复制标题
测试爱因斯坦方程的外边界处理
DOI：
--
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
M. Scheel
中科院分区：
文献类型：
--
作者：
O. Rinne;L. Lindblom;M. Scheel
用一个简单的测试问题来比较数值相对论中处理外边界的各种方法：一个具有外向引力波扰动的史瓦西黑洞。将使用不同边界处理计算的数值解与通过将外边界置于非常大的半径处获得的“参考”数值解进行比较。对于每个边界处理，将包含约束违反和提取引力波的完整解与参考解进行比较，从而评估人工边界引起的反射。这些测试基于爱因斯坦方程的一阶广义调和公式，并使用伪谱配置方法实现。回顾了该系统的约束保持边界条件，提出了一种改进的规范自由度边界条件。这里评估的备选边界条件包括冻结入射特征场、Sommerfeld边界条件以及Kreiss和Winicour的约束保持边界条件。不同的边界处理方法，如海绵层和空间致密化，也进行了测试。总的来说，这里发现的最佳处理方法结合了保留约束的边界条件，冻结Newman-Penrose标量Ψ0，并控制规范反射。
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 are based on a first-order generalized harmonic formulation of the Einstein equations and are implemented using a pseudo-spectral collocation method. 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 Ψ0, and control gauge reflections.