thornado-hydro：超新星流体动力学核状态方程间断Galerkin方法
thornado-hydro: a discontinuous Galerkin method for supernova hydrodynamics with nuclear equations of state
摘要：
本文介绍了高阶中微子辐射流体动力学工具包（thornado）中的非相对论流体动力学算法，该工具包正在开发用于核心坍缩超新星（CCSNe）的多物理场模拟以及与Runge-Kutta间断Galerkin（RKDG）方法相关的问题。更具体地说，thornado采用了光谱型节点配置近似，我们有扩展的限制器-斜率限制器，以防止非物理振荡和约束执行限制器，以防止非物理状态-从标准RKDG框架，能够容纳一个列表的核物质状态方程（EoS）。为了证明核EoS的算法的有效性，我们首先提出了在一个和两个空间维度的理想化设置中的基本测试问题的数值结果，采用笛卡尔坐标，球极坐标和圆柱坐标。然后，我们将RKDG方法应用于球对称的绝热坍缩、冲击波形成和冲击波传播问题，以15个太阳质量的祖先为起点。我们发现，扩展限制器提高了保真度和鲁棒性的RKDG方法在理想化的设置。边界执行限制器提高了鲁棒性的RKDG方法在绝热崩溃的应用，而我们发现，在特征字段的斜率限制是脆弱的EoS中的结构-更具体地说，在相变从核和核子散装核物质。这些应用的成功标志着在未来将RKDG方法应用于更真实的CCSN模拟的重要一步。
英文摘要：
This paper describes algorithms for non-relativistic 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 non-physical oscillations and a bound-enforcing limiter to prevent non-physical 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 solar mass progenitor. We find that the extended limiters improve the fidelity and robustness of the RKDG method in idealized settings. The bound-enforcing limiter improves 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.
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