This paper describes algorithms for nonrelativistic hydrodynamics in the toolkit for high-order neutrino radiation hydrodynamics (thornado), which is being developed for multiphysics simulations of core-collapse supernovae (CCSNe) and related problems with Runge–Kutta discontinuous Galerkin (RKDG) methods. More specifically, thornado employs a spectral-type nodal collocation approximation, and we have extended limiters—a slope limiter to prevent nonphysical oscillations and a bound-enforcing limiter to prevent nonphysical states—from the standard RKDG framework to be able to accommodate a tabulated nuclear equation of state (EoS). To demonstrate the efficacy of the algorithms with a nuclear EoS, we first present numerical results from basic test problems in idealized settings in one and two spatial dimensions, employing Cartesian, spherical-polar, and cylindrical coordinates. Then, we apply the RKDG method to the problem of adiabatic collapse, shock formation, and shock propagation in spherical symmetry, initiated with a 15 M _⊙ progenitor. We find that the extended limiters improve the fidelity and robustness of the RKDG method in idealized settings. The bound-enforcing limiter improves the robustness of the RKDG method in the adiabatic collapse application, while we find that slope limiting in characteristic fields is vulnerable to structures in the EoS—more specifically, in the phase transition from nuclei and nucleons to bulk nuclear matter. The success of these applications marks an important step toward applying RKDG methods to more realistic CCSN simulations with thornado in the future.

本文描述了用于高阶中微子辐射流体动力学（thornado）工具包中非相对论流体动力学的算法，该算法正在开发用于核塌陷超新星（CCSNe）的多物理场模拟以及与朗格-库塔不连续伽勒金法（RKDG）相关的问题。更具体地说，thornado采用了光谱类型的节点配位近似，并且我们从标准RKDG框架中扩展了限制器（用于防止非物理振荡的斜率限制器和用于防止非物理状态的束缚限制器），以便能够容纳列表状的核状态方程（ EoS）。为了证明具有核EoS的算法的有效性，我们首先介绍在笛卡尔坐标系，直角坐标系和圆柱坐标系下，在一维和二维空间中理想化设置下基本测试问题的数值结果。然后，我们应用RKDG方法绝热塌陷，形成冲击波，和冲击传播在球形对称，具有15发起的问题中号 _⊙祖细胞。我们发现，扩展的限制器可在理想设置下提高RKDG方法的保真度和鲁棒性。限界限制器提高了绝热塌陷应用中RKDG方法的鲁棒性，而我们发现特征场中的斜率限制容易受到EoS中结构的影响，更具体地说，是从核和核子到大核物质的相变。 。这些应用程序的成功标志着未来将RKDG方法应用于使用thornado进行更实际的CCSN仿真的重要一步。