Numerical {3 + 1} General Relativistic Hydrodynamics: A Local Characteristic Approach
Numerical {3 + 1} General Relativistic Hydrodynamics: A Local Characteristic Approach
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数值 {3 1} 广义相对论流体动力学：局部特征方法
DOI：
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发表时间：
1997
期刊：
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通讯作者：
J. Miralles
中科院分区：
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作者：
Francesc Banyuls;J. Font;J. Ibáñez;J. M. Martí;J. Miralles
我们提出了在{3 + 1}形式框架内数值求解三维广义相对论流体动力方程组的一般方法。这些方程被写成守恒形式，以利用它们的双曲特性。我们推导了建立基于局部黎曼问题解的数值格式所必需的理论成分。从而显式地给出了系统雅可比矩阵的谱分解，即特征值和特征向量。我们利用最近在闵可夫斯基时空中导出的相对论性黎曼问题的解析解，将众所周知的一系列标准激波管试验扩展到一般时空，作为校准任何氢码的重要工具。给出了球形和非球形吸积场景的选择，并与前人得到的相应解析解或数值解进行了比较。
We present a general procedure to solve numerically the three-dimensional general relativistic hydrodynamic system of equations within the framework of the {3 + 1} formalism. The equations are written in conservation form to exploit their hyperbolic character. We derive the theoretical ingredients that are necessary in order to build up a numerical scheme based on the solution of local Riemann problems. Hence the spectral decomposition of the Jacobian matrices of the system, i.e., the eigenvalues and eigenvectors, is explicitly shown. We have taken advantage of the analytic solution of the relativistic Riemann problem, recently derived in Minkowski spacetime, to extend the well-known battery of standard shock tube tests to general spacetimes as an important tool for calibrating any hydrocode. A selection of spherical and nonspherical accretion scenarios is presented and compared with the corresponding analytic or numerical solutions obtained by previous authors.