Roberts 流发电机在欧拉与拉格朗日代码中的收敛性
Convergence of Roberts flow dynamos in Eulerian and Lagrangian codes
- Leiden University（莱顿大学）
- Nordita, KTH Royal Institute of Technology and Stockholm University（北欧理论物理研究所，瑞典皇家理工学院与斯德哥尔摩大学）
- Stockholm University（斯德哥尔摩大学）
- Carnegie Mellon University（卡内基梅隆大学）
- Ilia State University（伊利亚国立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究验证 Roberts 流在 Pencil 与 SWIFT 代码中的数值收敛性，提出磁场可视化方法，并确立其作为磁流体动力学发电机基准的适用性。
AI中文摘要：
标准数值磁流体动力学代码的基准测试通常聚焦于一维和二维问题，这些测试忽略了发电机的可能性，即一种将动能转化为磁能的指数不稳定性。它们也往往忽略磁螺旋度守恒，而后者在周期域中可能产生显著影响。磁扩散的存在对发电机至关重要，例如，在使用欧拉势时无法找到发电机解，而在没有磁扩散的情况下，欧拉势是一种完全有效的方法。Roberts 流 I、II、III 和 IV 是支持三维发电机的二维流，所有这些流也都是大尺度发电机，因为它们的平面平均值具有显著强度，尽管流 II 在逐点上是非螺旋的。在此，我们展示了在 Pencil Code 中使用网格宽度的二阶、六阶和十阶离散格式获得的解的数值收敛性质，将结果与基于 SPH 的 SWIFT 代码进行比较，并提供一系列平均量，以方便将其用作基准来表征解。此外，我们提出了一种为所有 Roberts 流获得二维时间无关磁场可视化的方法，并在 Pencil 和 SWIFT 代码之间进行逐像素比较。这些特征的丰富组合使 Roberts 流成为磁流体动力学方程直接数值模拟的出色发电机基准。
英文摘要：
Standard benchmark tests for numerical magnetohydrodynamics codes focus on one- and two-dimensional problems that ignore the possibility of dynamos, i.e., an exponential instability converting kinetic energy into magnetic energy. They also tend to ignore magnetic helicity conservation that can have dramatic effects in periodic domains. The existence of magnetic diffusion is crucial for dynamos, as was exemplified by the impossibility of finding dynamo solutions when using Euler potentials, which is a perfectly valid approach in the absence of magnetic diffusion. The Roberts flows~I, II, III, and IV are two-dimensional flows that support three-dimensional dynamos, all of which are also large-scale dynamos in the sense that their planar averages are of significant strengths, even though flow~II is pointwise non-helical. Here we demonstrate the numerical convergence properties of solutions obtained using discretisation schemes of second, sixth, and tenth order in the mesh width in the Pencil Code, compare the results with the SPH-based SWIFT code, and present a list of averaged quantities that facilitate their use in characterising the solutions as benchmarks. In addition, we present a procedure to obtain two-dimensional time-independent magnetic field visualisation for all Roberts flows, and perform per-pixel comparison between the Pencil and SWIFT codes. The rich combination of features makes Roberts flows an excellent dynamo benchmark for the direct numerical simulations of magnetohydrodynamics equations.
