在广义相对论磁流体动力学程序Spritz中实现一种新的原始变量恢复方案
Implementing a new recovery scheme for primitive variables in the general relativistic magnetohydrodynamic code Spritz
摘要：
广义相对论磁流体动力学（GRMHD）模拟是研究双星中子星（BNS）和中子星（NS）-黑洞（BH）合并过程中各种潜在机制的基本工具。当代通量守恒GRMHD代码在数值上发展了一套基于“守恒”变量的守恒方程，然后需要将其转换回基本（“连续”）变量。相应的保守到原始变量的恢复过程，基于求根算法，构成了这样的GRMHD码的核心元素之一。最近，一种新的鲁棒，准确和高效的恢复方案称为RePrimAnd，它已经证明了总是收敛到一个唯一的解决方案的能力。该方案提供了细粒度的错误策略来处理由进化错误引起的无效状态，并为所有原始变量的错误提供了解析界。在这项工作中，我们描述了实施的RePrimAnd计划到GRMHD代码Spritz的技术方面。为了检查我们的实施以及评估该计划的各种功能，我们在三个维度上进行了一些GRMHD测试。我们的测试，其中包括关键的情况下，如NS崩溃的BH以及早期的演变（约50毫秒）的鱼骨Moncrief BH accrection磁盘系统，表明RePrimAnd能够支持磁化，低密度环境的磁流体压力比高达10^4，在以前使用的恢复方案失败的情况下。
英文摘要：
General relativistic magnetohydrodynamic (GRMHD) simulations represent a fundamental tool to probe various underlying mechanisms at play during binary neutron star (BNS) and neutron star (NS) - black hole (BH) mergers. Contemporary flux-conservative GRMHD codes numerically evolve a set of conservative equations based on `conserved' variables which then need to be converted back into the fundamental (`primitive') variables. The corresponding conservative-to-primitive variable recovery procedure, based on root-finding algorithms, constitutes one of the core elements of such GRMHD codes. Recently, a new robust, accurate and efficient recovery scheme called RePrimAnd was introduced, which has demonstrated the ability to always converge to a unique solution. The scheme provides fine-grained error policies to handle invalid states caused by evolution errors, and also provides analytical bounds for the error of all primitive variables. In this work, we describe the technical aspects of implementing the RePrimAnd scheme into the GRMHD code Spritz. To check our implementation as well as to assess the various features of the scheme, we perform a number of GRMHD tests in three dimensions. Our tests, which include critical cases such as a NS collapse to a BH as well as the early evolution (~50 ms) of a Fishbone-Moncrief BH-accrection disk system, show that RePrimAnd is able to support magnetized, low density environments with magnetic-to-fluid pressure ratios as high as 10^4, in situations where the previously used recovery scheme fails.
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