论文标题
通用辐射流体动力学的两端方案：系统描述和新应用
Two-moment scheme for general-relativistic radiation hydrodynamics: a systematic description and new applications
论文作者
论文摘要
我们在在隐性解释方案中实施两矩方案（IMEX）方案中的两矩方案时，我们提供了必要步骤的系统描述 - 以及将要遇到的潜在陷阱，以将辐射转移的贡献包括在一般偏变主义（磁磁）流体动力学的数值模拟中。我们利用M1闭合，该闭合为光学薄和厚的极限提供了精确的解决方案，并在这些极限之间进行了插值。特别注意新兴隐式保护方程组的有效解决方案。特别是，我们提出了一种有效的方法，可以通过IMEX方案中的$ 4 \ times 4 $ -matrix的反转来求解这些方程。尽管此方法依赖于几个近似值，但它在准确性和计算效率之间提供了很好的折衷。经过大量特殊相对论测试后，我们将新的辐射代码（\ texttt {frac}）与一般的相关磁含磁性水力动力学代码\ texttt {bhac}进行了研究，以研究辐射的米歇尔解决方案，即，在辐射范围内的黑洞中，球形的问题是在辐射范围内的黑洞上的问题。通过对此问题的参数空间进行最广泛的探索，我们发现可以通过体重，$ t $，发光度，$ l $和$ m $，$ \ varepsilon =（l/l _ {\ l/l _ {\ rm { edd}）/（\ dot {m}/\ dot {m} _ {\ rm edd}）= 7.41 \ times 10^{ - 7} \ left（t/10^6 \，\，\ mathrm {k} \ left（m/m_ \ odot \ right）^{0.48} $，其中$ l _ {\ mathrm {edd}} $和$ \ dot {m} _ {\ mathrm {edd}} $分别是Eddington luminosity和增生费率。最后，我们还考虑了从球形对称性的促进问题，发现该溶液在辐射场的扰动下是稳定的。
We provide a systematic description of the steps necessary -- and of the potential pitfalls to be encountered -- when implementing a two-moment scheme within an Implicit-Explicit (IMEX) scheme to include radiative-transfer contributions in numerical simulations of general-relativistic (magneto-)hydrodynamics. We make use of the M1 closure, which provides an exact solution for the optically thin and thick limit, and an interpolation between these limits. Special attention is paid to the efficient solution of the emerging set of implicit conservation equations. In particular, we present an efficient method for solving these equations via the inversion of a $4\times 4$-matrix within an IMEX scheme. While this method relies on a few approximations, it offers a very good compromise between accuracy and computational efficiency. After a large number of tests in special relativity, we couple our new radiation code, \texttt{FRAC}, with the general-relativistic magnetohydrodynamics code \texttt{BHAC} to investigate the radiative Michel solution, namely, the problem of spherical accretion onto a black hole in the presence of a radiative field. By performing the most extensive exploration of the parameter space for this problem, we find that the accretion's efficiency can be expressed in terms of physical quantities such as temperature, $T$, luminosity, $L$, and black-hole mass, $M$, via the expression $\varepsilon=(L/L_{\rm Edd})/(\dot{M}/\dot{M}_{\rm Edd})= 7.41\times 10^{-7}\left(T/10^6\,\mathrm{K}\right)^{0.22} \left(L/L_\odot\right)^{0.48} \left(M/M_\odot\right)^{0.48}$, where $L_{\mathrm{Edd}}$ and $\dot{M}_{\mathrm{Edd}}$ are the Eddington luminosity and accretion rate, respectively. Finally, we also consider the accretion problem away from spherical symmetry, finding that the solution is stable under perturbations in the radiation field.
