移动网格上的无散度磁流体动力学
Divergence-free magnetohydrodynamics on a moving mesh
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中文总结 AI 辅助
本文提出一种在移动网格上结合矢量势有限差分与有限体积的无散度MHD方法，实现伽利略不变性，并在AREPO中验证了高精度与稳定性。
中文摘要 AI 辅助
磁场在宇宙中无处不在，并在许多天体物理过程中发挥着重要作用，例如恒星形成和星系的演化。然而，考虑理想磁流体动力学（MHD）的流体动力学模拟方法面临着实现数值稳定性和物理一致性的挑战。两者都可能因磁场中非零局部散度误差的出现而受到损害。消除或减少这些离散化误差的不同方法已被广泛使用，包括约束输运或散度清理技术。然而，迄今为止，一种可以在拉格朗日代码中直接应用的无散度伽利略不变的MHD公式仍然是一个难以实现的目标。在这里，我们重新审视了在非结构化移动网格上使用矢量势来演化磁场的方法，并展示了特定的规范选择与适当离散化的积分方案相结合如何提供稳定且准确的MHD公式。我们的方法将单元中心矢量势的有限差分演化与其他流体量的有限体积表示相结合，并在移动网格代码AREPO中实现。新方法完全满足伽利略不变性，因此在经典问题（如场环平流）中显示出消失的误差。我们证明了我们的方案应用于各种测试问题以及3D实际应用时具有良好的准确性和稳定性，包括使用局部时间步长以及自适应网格细化和粗化时。
英文摘要
Magnetic fields are ubiquitous in the Universe and play an important role in many astrophysical processes, such as star formation and the evolution of galaxies. Hydrodynamical simulation methods that account for ideal magnetohydrodynamics (MHD) are however challenged by the need to achieve numerical stability and physical consistency. Both can be compromised by the occurrence of non-vanishing local divergence errors in the magnetic field. Different approaches to either eliminate or reduce these discretization errors are in widespread use, including constrained transport or divergence cleaning techniques. However, thus far a divergence-free Galilean invariant formulation of MHD that can be readily applied in Lagrangian codes has been an elusive goal. Here we revisit the use of the vector potential for evolving the magnetic field on an unstructured moving-mesh and show how a particular gauge choice combined with a suitably discretized integration scheme provides a stable and accurate formulation of MHD. Our method combines a finite-difference evolution of a cell-centred vector potential with a finite volume representation of the other fluid quantities, and is realized in the moving-mesh code AREPO. The new approach is fully Galilean invariant and therefore shows vanishing errors for classic problems such as field loop advection. We demonstrate good accuracy and stability when our scheme is applied to various test problems and to practical applications in 3D, including when local timesteps and adaptive mesh refinement and derefinement are used.
发表机构
- Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理研究所）
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