We describe a novel operator-splitting approach to numerical relativistic magnetohydrodynamics designed to expand its applicability to the domain of ultra-high magnetisation. In this approach, the electromagnetic field is split into the force-free component, governed by the equations of force-free degenerate electrodynamics (FFDE), and the perturbation component, governed by the perturbation equations derived from the full system of relativistic magnetohydrodynamics (RMHD). The combined system of the FFDE and perturbation equations is integrated simultaneously, for which various numerical techniques developed for hyperbolic conservation laws can be used. At the end of every time-step of numerical integration, the force-free and the perturbation components of the electromagnetic field are recombined and the result is regarded as the initial value of the force-free component for the next time-step, whereas the initial value of the perturbation component is set to zero. To explore the potential of this approach, we build a 3rd-order WENO code, which was used to carry out 1D and 2D test simulations. Their results show that this operator-splitting approach allows us to bypass the stiffness of RMHD in the ultra-high-magnetisation regime where the perturbation component becomes very small. At the same time, the cod

翻译：我们描述了一种新颖的算子分裂方法，用于数值求解相对论磁流体动力学，旨在将其适用性扩展到超高磁化区域。在这种方法中，电磁场被分为两部分：由无作用力退化电动力学（FFDE）方程支配的无作用力分量，以及由从完整相对论磁流体动力学（RMHD）系统推导出的扰动方程支配的扰动分量。FFDE方程和扰动方程的联合系统被同时积分，为此可以采用为双曲型守恒律开发的各种数值技术。在每个数值积分时间步结束时，电磁场的无作用力分量和扰动分量被重新组合，结果被视为下一时间步无作用力分量的初值，而扰动分量的初值则设为零。为了探索这种方法的潜力，我们构建了一个三阶WENO代码，并用于进行一维和二维测试模拟。结果表明，这种算子分裂方法使我们能够绕过RMHD在超高磁化状态下的刚性，其中扰动分量变得非常小。同时，该代码——