流体动力学中的时间隐式格式--它们在超相对论冲击波阵面区的优势
Time-implicit schemes in fluid dynamics? -- Their advantage in the regime of ultra-relativistic shock fronts
摘要：
相对论喷流是活动星系核和类星体的固有现象。据观察，它们也来自含有致密物体的系统，如白矮星、中子星和黑洞候选者。相应的洛伦兹因子，$Γ$，被发现与中心物体的紧凑性。在类星体和活动星系核的情况下，检测到等离子体的$Γ$因子大于$8$。然而，用$Γ\geq 4$数值一致地模拟传播激波阵面是一个困难的问题，因为用$Γ$时，输运算符的非线性显著增加，从而引起时间推进程序的数值停滞，或者它们可能完全发散。在本文中，我们提出了一个统一的数值求解器，用于模拟具有高洛伦兹因子的一维激波阵面的传播。该数值格式基于有限体积公式，具有自适应网格细化（AMR）和区域分解以进行并行计算。它统一了时间显式和时间隐式数值格式的框架内的预处理缺陷校正迭代求解过程。我们发现，时间隐式的解决方案的程序是显着优于他们的时间显式的同行在非常高的$Γ$制度，因此最适合一致的模拟活动星系核和微类星体的相对论外流。
英文摘要：
Relativistic jets are intrinsic phenomena of active galactic nuclei (AGN) and quasars. They have been observed to also emanate from systems containing compact objects, such as white dwarfs, neutron stars and black hole candidates. The corresponding Lorentz factors, $Γ$, were found to correlate with the compactness of the central objects. In the case of quasars and AGNs, plasmas with $Γ$-factors larger than $8$ were detected. However, numerically consistent modelling of propagating shock-fronts with $Γ\geq 4$ is a difficult issue, as the non-linearities underlying the transport operators increase dramatically with $Γ$, thereby giving rise to a numerical stagnation of the time-advancement procedure or alternatively they may diverge completely. In this paper, we present a unified numerical solver for modelling the propagation of one-dimensional shock fronts with high Lorentz factors. The numerical scheme is based on the finite-volume formulation with adaptive mesh refinement (AMR) and domain decomposition for parallel computation. It unifies both time-explicit and time-implicit numerical schemes within the framework of the pre-conditioned defect-correction iteration solution procedure. We find that time-implicit solution procedures are remarkably superior over their time-explicit counterparts in the very high $Γ$-regime and therefore most suitable for consistent modelling of relativistic outflows in AGNs and micro-quasars.
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