We present the first-ever moving-mesh general relativistic hydrodynamics solver for static spacetimes as implemented in the code, MANGA. Our implementation builds on the architectures of MANGA and the numerical relativity Python package NRPy+. We review the general algorithm to solve these equations and, in particular, detail the time stepping; Riemann solution across moving faces; conversion between primitive and conservative variables; validation and correction of hydrodynamic variables; and mapping of the metric to a Voronoi moving-mesh grid. We present test results for the numerical integration of an unmagnetized Tolman-Oppenheimer-Volkoff star for 24 dynamical times. We demonstrate that at a resolution of $10^6$ mesh generating points, the star is stable and its central density drifts downward by 2% over this timescale. At a lower resolution the central density drift increases in a manner consistent with the adopted second order spatial reconstruction scheme. These results agree well with the exact solutions, and we find the error behavior to be similar to Eulerian codes with second-order spatial reconstruction. We also demonstrate that the new code recovers the fundamental mode frequency for the same TOV star but with its initial pressure depleted by 10%

中文翻译：

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移动网格上的广义相对论流体动力学 I：静态时空

我们展示了第一个在代码 MANGA 中实现的静态时空移动网格广义相对论流体动力学求解器。我们的实现建立在 MANGA 的架构和数值相对论 Python 包 NRPy+ 之上。我们回顾了求解这些方程的一般算法，特别是详细介绍了时间步长；跨移动面的黎曼解；原始变量和保守变量之间的转换；水动力变量的验证和修正；并将度量映射到 Voronoi 移动网格。我们展示了一颗未磁化的 Tolman-Oppenheimer-Volkoff 星在 24 次动力学时间内的数值积分测试结果。我们证明，在 $10^6$ 网格生成点的分辨率下，恒星是稳定的，其中心密度在此时间尺度上向下漂移 2%。在较低分辨率下，中心密度漂移以与采用的二阶空间重建方案一致的方式增加。这些结果与精确解非常吻合，我们发现误差行为类似于具有二阶空间重建的欧拉码。我们还证明了新代码恢复了同一 TOV 星的基模频率，但其初始压力降低了 10%