General-relativistic neutron star evolutions with the discontinuous Galerkin method
General-relativistic neutron star evolutions with the discontinuous Galerkin method
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DOI：
10.1103/physrevd.98.044041
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发表时间：
2018-04
影响因子：
5
通讯作者：
F. H'ebert;Lawrence E. Kidder;S. Teukolsky
中科院分区：
文献类型：
--
作者：
F. H'ebert;Lawrence E. Kidder;S. Teukolsky
相对论流体力学的模拟通常需要高精度和强大的冲击处理性能。不连续伽辽金方法结合了这些特征——在解光滑的区域具有高阶收敛性，而在非光滑的区域具有激波捕获特性——以及几何灵活性，因此非常适合求解描述天体物理场景的偏微分方程。本文用不连续伽辽金方法给出了广义相对论中子星的演化。在这些模拟中，我们在同一个计算网格上同时发展时空几何和物质，这符合问题的球面几何。为了验证我们实现的正确性，我们执行标准收敛和冲击测试。然后我们展示了在三维空间中克尔黑洞演化的结果；在考林近似下的中子星（保持时空度量不变）；最后是中子星，它的时空和物质都是动态的。与同类分辨率的有限体积方法相比，该方法具有长期稳定性、良好的精度和提高的收敛速度。
Simulations of relativistic hydrodynamics often need both high accuracy and robust shock-handling properties. The discontinuous Galerkin method combines these features—a high order of convergence in regions where the solution is smooth and shock-capturing properties for regions where it is not—with geometric flexibility and is therefore well suited to solve the partial differential equations describing astrophysical scenarios. We present here evolutions of a general-relativistic neutron star with the discontinuous Galerkin method. In these simulations, we simultaneously evolve the spacetime geometry and the matter on the same computational grid, which we conform to the spherical geometry of the problem. To verify the correctness of our implementation, we perform standard convergence and shock tests. We then show results for evolving, in three dimensions, a Kerr black hole; a neutron star in the Cowling approximation (holding the spacetime metric fixed); and, finally, a neutron star where the spacetime and matter are both dynamical. The evolutions show long-term stability, good accuracy, and an improved rate of convergence versus a comparable-resolution finite-volume method.