The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A representative sample of available numerical schemes is discussed and particular emphasis is paid to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of relevant astrophysical simulations in strong gravitational fields, including gravitational collapse, accretion onto black holes and evolution of neutron stars, is also presented. ELECTRONIC SUPPLEMENTARY MATERIAL Supplementary material is available for this article at 10.12942/lrr-2000-2.

中文翻译：

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广义相对论中的数值流体动力学。

综述了理想广义相对论流体力学方程数值解的研究现状。提出了方程的不同公式，特别提到了非常适合先进数值方法的保守和双曲线公式。讨论了可用数值方案的代表性示例，并特别强调了基于通过线性黎曼求解器利用方程特征结构的方案的求解过程。还全面总结了强引力场中的相关天体物理模拟，包括引力塌缩、黑洞吸积和中子星演化。电子补充材料 本文的补充材料可在 10.12942/lrr-2000-2 上找到。