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arXiv 1912.06151astro-ph.HE
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使用燃烧限制器和自适应准统计平衡的多维超新星模拟中爆轰波的精确和有效的数值计算

An accurate and efficient numerical calculation of detonation waves in multidimensional supernova simulations using a burning limiter and adaptive quasi-statistical equilibrium

Doron Kushnir, Boaz Katz

摘要:

解决超新星中的热核爆炸波(TNDWs)的小长度尺度是目前不可能的多维全明星模拟。此外,多维模拟通常使用小的,过于简单的反应网络,并采用一个特设的核统计平衡(NSE)的过渡标准。由于应用的近似值的错误没有得到很好的理解。在这里,我们提出了一个新的准确和有效的数值方案,加速计算的数量级,并允许的结构的TNDWs被解决。数值方案有两个重要的组成部分:(1)燃烧限制器,它扩大了TNDW的宽度,同时精确地保留了其内部结构,(2)自适应地将同位素分离成处于核统计准平衡的基团,这解决了几乎平衡的反应的耗时燃烧计算。燃烧是在现场计算,采用所需的大型网络,而不使用后处理或预先描述TNDW背后的条件。特别地,自洽地计算接近和偏离NSE。该方案可以很容易地实现在多维代码。我们测试我们的计划对准确的解决方案的结构的TNDWs和对均匀扩展NSE。我们表明,分辨率是典型的多维全明星模拟,我们重现准确的热力学轨迹(密度,温度等)。对于已分辨的尺度(其中未应用燃烧限制器),精度优于百分之一,同时将未分辨的尺度(由燃烧限制器加宽)的误差保持在百分之几以内。

英文摘要:

Resolving the small length-scale of thermonuclear detonation waves (TNDWs) in supernovae is currently not possible in multidimensional full-star simulations. Additionally, multidimensional simulations usually use small, oversimplistic reaction networks and adopt an ad hoc transition criterion to nuclear statistical equilibrium (NSE). The errors due to the applied approximations are not well understood. We present here a new accurate and efficient numerical scheme that accelerates the calculations by orders of magnitudes and allows the structure of TNDWs to be resolved. The numerical scheme has two important ingredients: (1) a burning limiter that broadens the width of the TNDW while accurately preserving its internal structure, and (2) an adaptive separation of isotopes into groups that are in nuclear statistical quasi-equilibrium, which resolves the time-consuming burning calculation of reactions that are nearly balanced out. Burning is calculated in situ employing the required large networks without the use of post-processing or pre-describing the conditions behind the TNDW. In particular, the approach to and deviation from NSE are calculated self-consistently. The scheme can be easily implemented in multidimensional codes. We test our scheme against accurate solutions of the structure of TNDWs and against homogeneous expansion from NSE. We show that with resolutions that are typical for multidimensional full-star simulations, we reproduce the accurate thermodynamic trajectory (density, temperature, etc.) to an accuracy that is better than a percent for the resolved scales (where the burning limiter is not applied), while keeping the error for unresolved scales (broadened by the burning limiter) within a few percent.

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