We present a new methodology for simulating self-gravitating general-relativistic fluids. In our approach the fluid is modelled by means of Lagrangian particles in the framework of a general-relativistic (GR) smoothed particle hydrodynamics (SPH) formulation, while the spacetime is evolved on a mesh according to the Baumgarte–Shapiro–Shibata–Nakamura (BSSN) formulation that is also frequently used in Eulerian GR-hydrodynamics. To the best of our knowledge this is the first Lagrangian fully general relativistic hydrodynamics code (all previous SPH approaches used approximations to GR-gravity). A core ingredient of our particle–mesh approach is the coupling between the gas (represented by particles) and the spacetime (represented by a mesh) for which we have developed a set of sophisticated interpolation tools that are inspired by other particle–mesh approaches, in particular by vortex-particle methods. One advantage of splitting the methodology between matter and spacetime is that it gives us more freedom in choosing the resolution, so that—if the spacetime is smooth enough—we obtain good results already with a moderate number of grid cells and can focus the computational effort on the simulation of the matter. Further advantages of our approach are the ease with which ejecta can be tracked and the fact that the neutron star surface remains well-behaved and does not need any particular treatment. In the hydrodynamics part of the code we use a number of techniques that are new to SPH, such as reconstruction, slope limiting and steering dissipation by monitoring entropy conservation. We describe here in detail the employed numerical methods and demonstrate the code performance in a number of benchmark problems ranging from shock tube tests, over Cowling approximations to the fully dynamical evolution of neutron stars in self-consistently evolved spacetimes.

我们提出了一种模拟自引力广义相对论流体的新方法。在我们的方法中，流体在广义相对论 (GR) 平滑粒子流体动力学 (SPH) 公式的框架内通过拉格朗日粒子建模，而时空根据 Baumgarte-Shapiro-Shibata-Nakamura 在网格上演化（ BSSN) 公式也经常用于欧拉 GR 流体动力学。据我们所知，这是第一个拉格朗日完全广义相对论流体动力学代码（所有以前的 SPH 方法都使用近似 GR 引力）。我们的粒子网格方法的一个核心组成部分是气体（由粒子表示）和时空（由网格表示）之间的耦合，为此我们开发了一组受其他粒子网格方法启发的复杂插值工具，特别是通过涡流粒子方法。在物质和时空之间划分方法论的一个优点是它让我们在选择分辨率时有更多的自由，这样——如果时空足够平滑——我们已经用中等数量的网格单元获得了良好的结果，并且可以集中计算工作关于模拟的问题。我们方法的进一步优点是可以轻松跟踪喷射物，并且中子星表面保持良好状态并且不需要任何特殊处理。在代码的流体动力学部分，我们使用了许多 SPH 新的技术，例如重建、斜率限制和通过监测熵守恒的转向耗散。我们在此详细描述了所采用的数值方法，并在一系列基准问题中展示了代码性能，从激波管测试、Cowling 近似到自洽演化时空中中子星的完全动力学演化。