SYMMETRY WITHOUT SYMMETRY: NUMERICAL SIMULATION OF AXISYMMETRIC SYSTEMS USING CARTESIAN GRIDS
SYMMETRY WITHOUT SYMMETRY: NUMERICAL SIMULATION OF AXISYMMETRIC SYSTEMS USING CARTESIAN GRIDS
复制标题
没有对称的对称：使用笛卡尔网格的轴对称系统的数值模拟
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
J. Thornburg
中科院分区：
文献类型：
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作者：
M. Alcubierre;S. Brandt;B. Brügmann;D. Holz;E. Seidel;Ryoji Takahashi;J. Thornburg
提出了一种新的轴对称系统数值模拟方法。这种方法避免了使用柱面或极球坐标有限差分网格时经常出现的坐标奇异性，特别是在模拟像3+1数值相对论的张量偏微分方程组时。对于一个关于z轴的系统轴对称，基本思想是使用一个三维笛卡尔(x，y，z)坐标网格，它覆盖(比方说)y=0平面，但在y方向上只有一个有限差分子宽度。中心y=0网格面的场变量可以用法向(x，y，z)坐标有限差分来更新，而y≠0网格面的场变量可以通过轴对称假设和内插法由中心平面的场变量计算出来。我们在3+1数值广义相对论中的一组完全非线性测试计算中证明了该方法的有效性，其中包括黑洞和塌缩引力波。
We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used, particularly in simulating tensor partial differential equations like those of 3+1 numerical relativity. For a system axisymmetric about the z axis, the basic idea is to use a three-dimensional Cartesian(x,y,z) coordinate grid which covers (say) the y=0 plane, but is only one finite-difference-molecule–width thick in the y direction. The field variables in the central y=0 grid plane can be updated using normal (x,y,z)-coordinate finite differencing, while those in the y≠ 0 grid planes can be computed from those in the central plane by using the axisymmetry assumption and interpolation. We demonstrate the effectiveness of the approach on a set of fully nonlinear test computations in 3+1 numerical general relativity, involving both black holes and collapsing gravitational waves.