A discontinuous Galerkin method for general relativistic hydrodynamics in thornado
A discontinuous Galerkin method for general relativistic hydrodynamics in thornado
复制标题
DOI：
10.1088/1742-6596/1623/1/012012
复制
发表时间：
2020-09
期刊：
影响因子：
--
通讯作者：
S. Dunham;E. Endeve;A. Mezzacappa;Jesse Buffaloe;K. Holley-Bockelmann
中科院分区：
文献类型：
--
作者：
S. Dunham;E. Endeve;A. Mezzacappa;Jesse Buffaloe;K. Holley-Bockelmann
不连续伽辽金（DG）方法提供了一种在光滑流体流动区域获得高阶精确解的方法，同时仍然可以解决强冲击。这些和其他性质使得DG方法对于解决涉及流体动力学的问题具有吸引力；例如，核心坍缩超新星问题。考虑到这一点，我们正在开发一个DG求解器，用于广义相对论，在3+1时空分解下的理想流体动力学方程，假设广义相对论的保形平坦近似。在限制器的帮助下，我们用几个困难的测试问题验证了我们的代码的准确性和鲁棒性：一个特殊相对论Kelvin-Helmholtz不稳定性问题，一个二维特殊相对论Riemann问题，以及一个一维和二维广义相对论立吸积激波（SAS）问题。我们发现在可用的情况下，与已发表的结果有很好的一致性。我们还建立了一维SAS问题的充分解决方案，并在二维的常设吸积冲击不稳定性（SASI）方面找到了令人鼓舞的结果。
Discontinuous Galerkin (DG) methods provide a means to obtain high-order accurate solutions in regions of smooth fluid flow while still resolving strong shocks. These and other properties make DG methods attractive for solving problems involving hydrodynamics; e.g., the core-collapse supernova problem. With that in mind we are developing a DG solver for the general relativistic, ideal hydrodynamics equations under a 3+1 decomposition of spacetime, assuming a conformally-flat approximation to general relativity. With the aid of limiters we verify the accuracy and robustness of our code with several difficult test-problems: a special relativistic Kelvin-Helmholtz instability problem, a two-dimensional special relativistic Riemann problem, and a one- and two-dimensional general relativistic standing accretion shock (SAS) problem. We find good agreement with published results, where available. We also establish sufficient resolution for the 1D SAS problem and find encouraging results regarding the standing accretion shock instability (SASI) in 2D.