各向异性辐射场与相对论电阻性磁流体耦合的数值处理
Numerical Treatment of Anisotropic Radiation Field Coupling with the Relativistic Resistive Magnetofluids
摘要：
本文发展了一种求解完全狭义相对论电阻辐射磁流体力学的数值方法。我们的代码保证总质量，动量和能量守恒。辐射能量密度和辐射通量的一致更新使用M-1封闭方法，它可以解决一个各向异性的辐射场相比，爱丁顿近似以及通量限制扩散近似。对于电阻部分，我们采用欧姆定律的简单形式。对流项用近似的Riemann解显式求解，主要是HLL格式，并进行了一些试验的HLLC和HLLD格式。的源项，它描述了气体辐射相互作用和磁能量耗散，隐式集成，放松柯朗-弗里德里希-路易条件，即使在光学厚制度或大的磁雷诺数制度。虽然我们需要在每个网格点上反演$4\times 4$（用于气体-辐射相互作用）和$3\times 3$（用于磁能量耗散）矩阵以进行隐式积分，但它们是解析地获得的，而不妨碍大规模并行计算。我们表明，我们的代码给出了合理的结果，在理想的磁流体力学，传播辐射，辐射流体力学的数值试验。我们还将我们的电阻程序应用于相对论Petschek型磁重联，揭示了辐射阻力对重联率的影响。
英文摘要：
We develop a numerical scheme for solving a fully special relativistic resistive radiation magnetohydrodynamics. Our code guarantees conservations of total mass, momentum and energy. Radiation energy density and radiation flux are consistently updated using the M-1 closure method, which can resolve an anisotropic radiation fields in contrast to the Eddington approximation as well as the flux-limited diffusion approximation. For the resistive part, we adopt a simple form of the Ohm's law. The advection terms are explicitly solved with an approximate Riemann solver, mainly HLL scheme, and HLLC and HLLD schemes for some tests. The source terms, which describe the gas-radiation interaction and the magnetic energy dissipation, are implicitly integrated, relaxing the Courant-Friedrichs-Lewy condition even in optically thick regime or a large magnetic Reynolds number regime. Although we need to invert $4\times 4$ (for gas-radiation interaction) and $3\times 3$ (for magnetic energy dissipation) matrices at each grid point for implicit integration, they are obtained analytically without preventing massive parallel computing. We show that our code gives reasonable outcomes in numerical tests for ideal magnetohydrodynamics, propagating radiation, and radiation hydrodynamics. We also applied our resistive code to the relativistic Petschek type magnetic reconnection, revealing the reduction of the reconnection rate via the radiation drag.
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