Numerical relativity in spherical polar coordinates: Off-center simulations
Numerical relativity in spherical polar coordinates: Off-center simulations
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球极坐标中的数值相对论：偏心模拟
DOI：
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发表时间：
2015
期刊：
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通讯作者：
E. Muller
中科院分区：
文献类型：
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作者：
T. Baumgarte;P. J. Montero;E. Muller
我们最近提出了一种新的方法，在球极坐标系中对真空和相对论流体力学进行数值相对论模拟。我们的方法基于BSSN方程的参考度量公式，所有张量分量的因式分解，以及部分隐式龙格-库塔方法，并且不依赖于方程的正则化，也不对原点上的对称性做出任何假设。为了证明这一特征，我们在这里提出了几个偏离中心的模拟，包括单个黑洞和中子星的模拟，其中心远离坐标系统的原点，以及两个黑洞的不对称正面碰撞。我们还重温了相对论流体力学的实现，并证明了流体力学的参考度量公式与所有张量分量的分解一起避免了与原点和轴上的坐标奇点相关的问题。作为一个特别苛刻的测试，我们给出了冲击波通过球面极坐标系原点传播的结果。
We have recently presented a new approach for numerical relativity simulations in spherical polar coordinates, both for vacuum and for relativistic hydrodynamics. Our approach is based on a reference-metric formulation of the BSSN equations, a factoring of all tensor components, as well as a partially implicit Runge-Kutta method, and does not rely on a regularization of the equations, nor does it make any assumptions about the symmetry across the origin. In order to demonstrate this feature we present here several off-centered simulations, including simulations of single black holes and neutron stars whose center is placed away from the origin of the coordinate system, as well as the asymmetric head-on collision of two black holes. We also revisit our implementation of relativistic hydrodynamics and demonstrate that a reference-metric formulation of hydrodynamics together with a factoring of all tensor components avoids problems related to the coordinate singularities at the origin and on the axes. As a particularly demanding test we present results for a shock wave propagating through the origin of the spherical polar coordinate system.