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首页> 外文期刊>Journal of Computational Physics >A robust numerical scheme for highly compressible magnetohydrodynamics: Nonlinear stability, implementation and tests
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A robust numerical scheme for highly compressible magnetohydrodynamics: Nonlinear stability, implementation and tests

机译：高度可压缩的磁流体动力学的鲁棒数值方案：非线性稳定性，实现和测试

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摘要

The ideal MHD equations are a central model in astrophysics, and their solution relies upon stable numerical schemes. We present an implementation of a new method, which possesses excellent stability properties. Numerical tests demonstrate that the theoretical stability properties are valid in practice with negligible compromises to accuracy. The result is a highly robust scheme with state-of-the-art efficiency. The scheme's robustness is due to entropy stability, positivity and properly discretised Powell terms. The implementation takes the form of a modification of the MHD module in the FLASH code, an adaptive mesh refinement code. We compare the new scheme with the standard FLASH implementation for MHD. Results show comparable accuracy to standard FLASH with the Roe solver, but highly improved efficiency and stability, particularly for high Mach number flows and low plasma β. The tests include 1D shock tubes, 2D instabilities and highly supersonic, 3D turbulence. We consider turbulent flows with RMS sonic Mach numbers up to 10, typical of gas flows in the interstellar medium. We investigate both strong initial magnetic fields and magnetic field amplification by the turbulent dynamo from extremely high plasma β. The energy spectra show a reasonable decrease in dissipation with grid refinement, and at a resolution of 512~3 grid cells we identify a narrow inertial range with the expected power law scaling. The turbulent dynamo exhibits exponential growth of magnetic pressure, with the growth rate higher from solenoidal forcing than from compressive forcing. Two versions of the new scheme are presented, using relaxation-based 3-wave and 5-wave approximate Riemann solvers, respectively. The 5-wave solver is more accurate in some cases, and its computational cost is close to the 3-wave solver.
机译：理想的MHD方程是天体物理学的中心模型，其求解依赖于稳定的数值方案。我们提出了一种新方法的实现，该方法具有出色的稳定性。数值测试表明，理论上的稳定性能在实践中是有效的，对精度的影响可以忽略不计。结果是具有最先进效率的高度健壮的方案。该方案的鲁棒性归因于熵的稳定性，正性和适当离散的鲍威尔项。该实现形式是对FLASH代码（一种自适应网格细化代码）中的MHD模块进行修改的形式。我们将新方案与用于MHD的标准FLASH实现进行了比较。结果表明，使用Roe求解器的精度与标准FLASH相当，但效率和稳定性得到了极大提高，尤其是对于高马赫数流量和低血浆β而言。测试包括1D冲击管，2D不稳定性和高超声速3D湍流。我们考虑RMS声马赫数最高为10的湍流，这是星际介质中典型的气流。我们研究了来自极高血浆β的强初始磁场和湍流发电机产生的磁场放大。能谱显示出随着网格细化合理地降低了耗散，并且在512〜3个网格单元的分辨率下，我们确定了一个窄的惯性范围，具有预期的幂律定标。湍流的发电机表现出磁压力的指数增长，其中螺线管强迫的增长速度高于压迫压力的增长速度。提出了新方案的两个版本，分别使用基于松弛的3波和5波近似Riemann求解器。 5波求解器在某些情况下更精确，其计算成本接近3波求解器。

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