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arXiv 1001.4841astro-ph.SRgr-qc
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核心坍缩超新星的一个新的多维广义相对论中微子流体动力学程序。I.球对称的方法和代码测试

A new multi-dimensional general relativistic neutrino hydrodynamics code for core-collapse supernovae. I. Method and code tests in spherical symmetry

B. Mueller, H. -Th. Janka, H. Dimmelmeier

摘要:

提出了一个新的广义相对论(GR)程序,用于流体动力学超新星模拟,其中中微子输运在球对称和方位对称(1D/2D)下进行。该代码是CoCoNuT hydro模块的组合,该模块是基于黎曼解算器的高分辨率激波捕获方法,以及三味,能量依赖的中微子输运方案VERTEX。VERTEX将中微子矩方程与从模型玻尔兹曼方程计算的可变爱丁顿因子闭合相结合,并在2D中使用逐射线加近似,假设中微子分布围绕径向轴对称,因此中微子通量是径向的。我们的时空处理采用ADM 3+1形式主义与共形平坦性条件的空间三度规。这种方法在1D中是精确的,并且已经被证明对旋转恒星坍缩也能产生非常精确的结果。我们引入新的配方的能量方程,以提高总能量守恒的相对论和牛顿流体模拟与欧拉有限体积代码。此外,一个修改版本的VERTEX计划,同时保持能量和轻子数具有更好的精度和更高的数值稳定性。为了验证我们的代码,我们进行了一系列的测试,包括详细的比较与发表的一维结果恒星核心崩溃。原始中子星冷却超过几秒钟的长时间模拟都证明了新的CoCoNuT-VERTEX代码的鲁棒性,并显示了GR效应的近似处理的有效引力势PROMETHEUS-VERTEX是非常准确的一维。(节略)

英文摘要:

We present a new general relativistic (GR) code for hydrodynamic supernova simulations with neutrino transport in spherical and azimuthal symmetry (1D/2D). The code is a combination of the CoCoNuT hydro module, which is a Riemann-solver based, high-resolution shock-capturing method, and the three-flavor, energy-dependent neutrino transport scheme VERTEX. VERTEX integrates the neutrino moment equations with a variable Eddington factor closure computed from a model Boltzmann equation and uses the ray-by-ray plus approximation in 2D, assuming the neutrino distribution to be axially symmetric around the radial direction, and thus the neutrino flux to be radial. Our spacetime treatment employs the ADM 3+1 formalism with the conformal flatness condition for the spatial three-metric. This approach is exact in 1D and has been shown to yield very accurate results also for rotational stellar collapse. We introduce new formulations of the energy equation to improve total energy conservation in relativistic and Newtonian hydro simulations with Eulerian finite-volume codes. Moreover, a modified version of the VERTEX scheme is developed that simultaneously conserves energy and lepton number with better accuracy and higher numerical stability. To verify our code, we conduct a series of tests, including a detailed comparison with published 1D results for stellar core collapse. Long-time simulations of proto-neutron star cooling over several seconds both demonstrate the robustness of the new CoCoNuT-VERTEX code and show the approximate treatment of GR effects by means of an effective gravitational potential as in PROMETHEUS-VERTEX to be remarkably accurate in 1D. (abridged)

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