A SECOND-ORDER GODUNOV METHOD FOR MULTI-DIMENSIONAL RELATIVISTIC MAGNETOHYDRODYNAMICS
A SECOND-ORDER GODUNOV METHOD FOR MULTI-DIMENSIONAL RELATIVISTIC MAGNETOHYDRODYNAMICS
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DOI：
10.1088/0067-0049/193/1/6
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发表时间：
2011-01
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影响因子：
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通讯作者：
K. Beckwith;J. Stone
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作者：
K. Beckwith;J. Stone
我们描述了一个新的Goddom算法相对论磁流体力学（RMHD），结合了一个简单的，不可分割的二阶精度积分器与约束运输（CT）的方法，强制执行螺线管约束的磁场。各种近似黎曼解算器实现计算守恒变量的通量。该方法进行了测试，一套全面的多维问题。这些测试帮助我们开发了一个层次的校正步骤，应用时，集成算法预测非物理状态，由于错误的通量，或保守和原始变量之间的反演错误。虽然很少使用，但这些校正显著提高了算法的稳定性。我们提出了这些算法的应用程序中的两个问题RMHD的初步结果：超音速磁化射流的传播和磁场的放大由相对论开尔文-亥姆霍兹不稳定性（KHI）驱动的湍流。这两个应用程序揭示了重要的差异与黎曼解算器，采用不同的近似通量计算的结果。例如，我们表明，使用黎曼解算器，包括接触和旋转的不连续性，可以增加茧内的磁场强度的一个因素，10在RMHD射流的模拟，可以增加光谱分辨率的三维RMHD湍流驱动的KHI的一个因素。这种准确性的提高远远超过了计算成本的相关增加。我们的RMHD方案作为Athena代码的一部分公开提供。
We describe a new Godunov algorithm for relativistic magnetohydrodynamics (RMHD) that combines a simple, unsplit second-order accurate integrator with the constrained transport (CT) method for enforcing the solenoidal constraint on the magnetic field. A variety of approximate Riemann solvers are implemented to compute the fluxes of the conserved variables. The methods are tested with a comprehensive suite of multi-dimensional problems. These tests have helped us develop a hierarchy of correction steps that are applied when the integration algorithm predicts unphysical states due to errors in the fluxes, or errors in the inversion between conserved and primitive variables. Although used exceedingly rarely, these corrections dramatically improve the stability of the algorithm. We present preliminary results from the application of these algorithms to two problems in RMHD: the propagation of supersonic magnetized jets and the amplification of magnetic field by turbulence driven by the relativistic Kelvin–Helmholtz instability (KHI). Both of these applications reveal important differences between the results computed with Riemann solvers that adopt different approximations for the fluxes. For example, we show that the use of Riemann solvers that include both contact and rotational discontinuities can increase the strength of the magnetic field within the cocoon by a factor of 10 in simulations of RMHD jets and can increase the spectral resolution of three-dimensional RMHD turbulence driven by the KHI by a factor of two. This increase in accuracy far outweighs the associated increase in computational cost. Our RMHD scheme is publicly available as part of the Athena code.