An implementation of the microphysics in full general relativity: a general relativistic neutrino leakage scheme
An implementation of the microphysics in full general relativity: a general relativistic neutrino leakage scheme
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完全广义相对论中微观物理的实现：广义相对论中微子泄漏方案
DOI：
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Yuichiro Sekiguchi
中科院分区：
文献类型：
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作者：
Yuichiro Sekiguchi
进行考虑微物理过程(如弱相互作用和中微子冷却)的完全广义相对论模拟是数值相对论长期存在的问题之一。在广义相对论框架下实现弱相互作用的主要困难之一在于热致密物质中弱相互作用过程的特征时间标度(WP时间标度)比动力学时间标度(Tdyn)短得多。在数值上，这意味着刚性源项出现在方程中，因此通常需要隐式格式来稳定地求解相关方程。否则，将需要非常短的时间步长(Δt<；twp≪tdyn)来显式地求解它们，这在目前的计算资源中是不现实的。此外，在相对论框架下，洛伦兹因子与静止质量密度和能量密度耦合。比热容也与动量相关联。由于这些耦合，从守恒量恢复本原变量和洛伦兹因子是非常复杂的。因此，在完全广义相对论框架下隐式求解这些方程是非常困难的。在目前的情况下，除了球对称的情况外，还没有提出任何隐式方法。因此，本文在完全广义相对论框架下发展了一种近似显式程序，作为向更现实的复杂模型的微物理的第一次实现。该程序基于所谓的中微子泄漏方案，该方案基于中微子从系统中泄漏出来的特征时间标度(泄漏时间标度)远远长于WP时间标度的特性。然而，在以往的泄漏方案中，人为地避免了源项僵硬的问题。在这篇文章中，我给出了一个详细的中微子泄漏方案和一个在完全广义相对论框架下显式求解方程的简单而稳定的方法。改进了人工处理刚性源项的缺点。我还进行了测试仿真，以检查本方法的有效性，表明它工作得很好。
Performing fully general relativistic simulations taking account of microphysical processes (e.g. weak interactions and neutrino cooling) is one of the long-standing problems in numerical relativity. One of main difficulties in implementation of weak interactions in the general relativistic framework lies in the fact that the characteristic timescale of weak interaction processes (the WP timescale, ) in hot dense matters is much shorter than the dynamical timescale (tdyn). Numerically this means that stiff source terms appear in the equations so that an implicit scheme is in general necessary to stably solve the relevant equations. Otherwise a very short timestep (Δt < twp ≪ tdyn) will be required to solve them explicitly, which is unrealistic in the present computational resources. Furthermore, in the relativistic framework, the Lorentz factor is coupled with the rest mass density and the energy density. The specific enthalpy is also coupled with the momentum. Due to these couplings, it is very complicated to recover the primitive variables and the Lorentz factor from conserved quantities. Consequently, it is very difficult to solve the equations implicitly in the fully general relativistic framework. At the current status, no implicit procedure has been proposed except for the case of the spherical symmetry. Therefore, an approximate explicit procedure is developed in the fully general relativistic framework in this paper as a first implementation of the microphysics toward a more realistic sophisticated model. The procedure is based on the so-called neutrino leakage schemes which are based on the property that the characteristic timescale in which neutrinos leak out of the system (the leakage timescale, tleak) is much longer than the WP timescale. In the previous leakage schemes, however, the problems of the stiff source terms are avoided in an artificial manner. In this paper, I present a detailed neutrino leakage scheme and a simple and stable method for solving the equations explicitly in the fully general relativistic framework. The drawback of the artificial treatment of the stiff source terms is improved. I also perform a test simulation to check the validity of the present method, showing that it works fairly well.
DOI：
10.1088/0004-637x/694/1/664
发表时间：
2007-08
期刊：
The Astrophysical Journal
影响因子：
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作者：
A. Marek;H. Janka
通讯作者：
A. Marek;H. Janka
影响因子：
8.6
作者：
H. Dimmelmeier;C. Ott;H.-Th. Janka;A. Marek;E. Müller
通讯作者：
E. Müller