基于ADER-WENO预估和多维Riemann校正的亚光速相对论磁流体力学方案
A Subluminal Relativistic Magnetohydrodynamics Scheme with ADER-WENO Predictor and Multidimensional Riemann Solver-Based Corrector
摘要：
相对论性磁流体动力学（RMHD）方程组最近在天体物理计算中得到了越来越多的应用。即便如此，RMHD代码仍然很脆弱。重建有时会在网格的某些部分产生超光速。在本文中，我们提出了一种重建策略，克服了这个问题，使一个单一的保守的原始转换每个细胞，然后高阶WENO重建一组精心选择的原语，保证亚光速重建的流量变量。对于通过预测步骤的时间演化，我们还提出了二阶，三阶和四阶精确的ADER方法，保持速度在预测步骤。RMHD系统还要求磁场以无发散的方式演化。在经典数值MHD的治疗类似的问题已经看到了最近的进展与多维黎曼解的出现。通过开发RMHD的多维黎曼解算器，我们表明，类似的进步延伸到RMHD。结果，在校正步骤中使用边缘中心电场可以更精确地演化面中心磁场。这些边缘中心的电场来自一个多维黎曼求解RMHD，我们在本文中提出。在本文中，我们还开发了几个新的测试问题RMHD。我们表明，RMHD涡可以设计的计算网格上传播的自我保护的结构。这些RMHD涡测试问题提供了一种手段，做真正的多维精度测试RMHD代码。其他几个严格的测试问题。我们在某些测试问题的分辨率的重要性。我们的测试包括一个演示，RMHD涡是稳定的，当他们与冲击相互作用。
英文摘要：
The relativistic magnetohydrodynamics (RMHD) set of equations has recently seen increased use in astrophysical computations. Even so, RMHD codes remain fragile. The reconstruction can sometimes yield superluminal velocities in certain parts of the mesh. In this paper we present a reconstruction strategy that overcomes this problem by making a single conservative to primitive transformation per cell followed by higher order WENO reconstruction on a carefully chosen set of primitives that guarantee subluminal reconstruction of the flow variables. For temporal evolution via a predictor step we also present second, third and fourth order accurate ADER methods that keep the velocity subluminal during the predictor step. The RMHD system also requires the magnetic field to be evolved in a divergence-free fashion. In the treatment of classical numerical MHD the analogous issue has seen much recent progress with the advent of multidimensional Riemann solvers. By developing multidimensional Riemann solvers for RMHD, we show that similar advances extend to RMHD. As a result, the face-centered magnetic fields can be evolved much more accurately using the edge-centered electric fields in the corrector step. Those edge-centered electric fields come from a multidimensional Riemann solver for RMHD which we present in this paper. In this paper we also develop several new test problems for RMHD. We show that RMHD vortices can be designed that propagate on the computational mesh as self-preserving structures. These RMHD vortex test problems provide a means to do truly multidimensional accuracy testing for RMHD codes. Several other stringent test problems are presented. We show the importance of resolution in certain test problems. Our tests include a demonstration that RMHD vortices are stable when they interact with shocks.
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