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 multidimensional 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 use of Riemann solvers which include both contact and rotational discontinuities can increase the strength of the magnetic field within the cocoon by a factor of ten in simulations of RMHD jets, and can increase the spectral resolution of three-dimensional RMHD turbulence driven by the KHI by a factor of 2. This increase in accuracy far outweighs the associated increase in computational cost. Our RMHD scheme is publicly available as part of the Athena code.
Exact Riemann solver for ideal magnetohydrodynamics that can handle all types of intermediate shocks and switch-on/off waves
我们建立了一个程序，可以在任意初始条件下得到理想磁流体力学（MHD）中黎曼问题的精确解。该程序不仅可以处理规则波，而且可以处理开关稀疏波和所有类型的非规则波：中间波和开关波。此外，尽管代码部分基于Torrilhon（2002）提出的算法（Torrilhon 2002 Exact Solver and Uniform Condition for Riemann problems of Ideal Magnetohydrodynamics. Research report 2002-06，Seminar for Applied Mathematics，ETH，Zurich），其不能处理所有类型的非规则波，也不能处理没有正常或横向磁场的初始条件。我们的求解器可以找到一个给定的黎曼问题的所有解决方案，因此，如本文所示，可以详细研究的解决方案空间的结构。因此，求解器是解决MHD黎曼问题解的存在唯一性这一突出问题的有力工具。此外，求解器可能会被应用到数值MHD格式，如Goddom计划在未来。
A High-Order Relativistic Two-Fluid Electrodynamic Scheme with Consistent Reconstruction of Electromagnetic Fields and a Multidimensional Riemann Solver for Electromagnetism
PANGU I: A Parthenon-Based Framework for Fixed-Spacetime GRMHD
School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）；School of Physics, Peking University（北京大学物理学院）；Key Laboratory of Multiscale Spin Physics, Ministry of Education（教育部多尺度自旋物理重点实验室）；School of Physical Science and Technology, Ningbo University（宁波大学物理科学与技术学院）
A Multidimensional General-Relativistic Boltzmann Solver for Neutrino Transport: Implementation, Discretization and Optimization
KU Leuven（荷语鲁汶大学）；California Institute of Technology（加州理工学院）；University of California, Berkeley（加州大学伯克利分校）；University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）
A Necessary Condition for the Submergence of Proto-Neutron Star Magnetic Fields by Supernova Fallback
Osaka University（大阪大学）；The University of Tokyo（东京大学）；Musashino Art University（武藏野美术大学）；Tohoku University（东北大学）；California Institute of Technology（加州理工学院）；Komazawa University（驹泽大学）
