基于WENO的高阶交错Godunov型约束输运格式求解无力电动力学
A High-Order WENO-based Staggered Godunov-type Scheme with Constrained Transport for Force-free Electrodynamics
摘要：
磁流体力学（MHD）的无力（或低惯性）极限可以应用于许多天体，包括黑洞、中子星和吸积盘，这些天体的电磁场非常强，以至于等离子体的惯性和压力可以忽略不计。这是很难实现的标准MHD数值方法，因为他们仍然要处理等离子体惯性项，即使这些条款是远远小于电磁条款。在无力近似下，等离子体动力学完全由磁场决定。等离子体提供了电磁场动力学所需的电流和电荷密度，但这些电流没有惯性。我们提出了一个高阶Goddom方案来研究这种无力电动力学。我们已经实现了加权基本无振荡（WENO）空间插值在我们的计划。一个精确的黎曼求解器的实施，这需要频谱分解成特征波。我们提出了磁场与约束运输（CT）计划，以保持发散自由的条件，机器舍入误差。时间积分采用三阶TVD龙格-库塔格式。从面为中心的变量到体积为中心的变量的映射被仔细考虑。进行了广泛的测试，以证明我们的计划，以正确地解决无力电动力学的能力。最后，我们应用该方案研究了相对论性磁主导撕裂不稳定性和中子星磁层。
英文摘要：
The force-free (or low inertia) limit of magnetohydrodynamics (MHD) can be applied to many astrophysical objects, including black holes, neutron stars, and accretion disks, where the electromagnetic field is so strong that the inertia and pressure of the plasma can be ignored. This is difficult to achieve with the standard MHD numerical methods because they still have to deal with plasma inertial terms even when these terms are much smaller than the electromagnetic terms. Under the force free approximation, the plasma dynamics is entirely determined by the magnetic field. The plasma provides the currents and charge densities required by the dynamics of electromagnetic fields, but these currents carry no inertia. We present a high order Godunov scheme to study such force-free electrodynamics. We have implemented weighted essentially non-oscillatory (WENO) spatial interpolations in our scheme. An exact Riemann solver is implemented, which requires spectral decomposition into characteristic waves. We advance the magnetic field with the constrained transport (CT) scheme to preserve the divergence free condition to machine round-off error. We apply the third order total variation diminishing (TVD) Runge-Kutta scheme for the temporal integration. The mapping from face-centered variables to volume-centered variables is carefully considered. Extensive testing are performed to demonstrate the ability of our scheme to address force-free electrodynamics correctly. We finally apply the scheme to study relativistic magnetically dominated tearing instabilities and neutron star magnetospheres.
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