论文标题
索纳多的一般相对论流体动力学的不连续的galerkin方法
A Discontinuous Galerkin Method for General Relativistic Hydrodynamics in thornado
论文作者
论文摘要
不连续的Galerkin（DG）方法提供了一种在光滑流体流动区域获得高阶准确溶液的方法，而借助限制器仍可以解决强烈的冲击。这些和其他特性使DG方法具有解决涉及流体动力学的问题的吸引力。例如，核心爆发超新星问题。考虑到这一点，我们正在为一般相对论，理想的流体动力学方程在3+1的时空分解下开发DG求解器，假设与一般相对性相连近似。在限制器的帮助下，我们使用几个困难的测试问题来验证代码的准确性和鲁棒性：一种特殊的相对论开尔文 - 赫尔姆霍尔兹不稳定性问题，二维特殊的特殊相对论的利曼问题，以及一种和二维的一般相对论驻留式积分冲击（SAS）问题。我们发现与已发表的结果达成了很好的共识。我们还为1D SAS问题建立了足够的解决方案，并在2D中找到了关于常规吸积冲击不稳定性（SASI）的令人鼓舞的结果。
Discontinuous Galerkin (DG) methods provide a means to obtain high-order accurate solutions in regions of smooth fluid flow while, with the aid of limiters, 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.
