This paper develops novel and robust central discontinuous Galerkin (CDG) schemes of arbitrarily high-order accuracy for special relativistic magnetohydrodynamics (RMHD) with a general equation of state (EOS). These schemes are provably bound-preserving (BP), i.e., consistently preserve the upper bound for subluminal fluid velocity and the positivity of density and pressure, while also (locally) maintaining the divergence-free (DF) constraint for the magnetic field. For 1D RMHD, the standard CDG method is exactly DF, and its BP property is proven under a condition achievable by BP limiter. For 2D RMHD, we design provably BP and locally DF CDG schemes based on the suitable discretization of a modified RMHD system. A key novelty in our schemes is the discretization of additional source terms in the modified RMHD equations, so as to precisely counteract the influence of divergence errors on the BP property across overlapping meshes. We provide rigorous proofs of the BP property for our CDG schemes and first establish the theoretical connection between BP and discrete DF properties on overlapping meshes for RMHD. Owing to the absence of explicit expressions for primitive variables in terms of conserved variables, the constraints of physical bounds are strongly nonlinear, making the BP proofs highly nontrivial. We overcome these challenges through technical estimates within the geometric quasilinearization (GQL) framework, which converts the nonlinear constraints into linear ones. Furthermore, we introduce a new 2D cell average decomposition on overlapping meshes, which relaxes the theoretical BP CFL constraint and reduces the number of internal nodes, thereby enhancing the efficiency of the 2D BP CDG method. We implement the proposed CDG schemes for extensive RMHD problems with various EOSs, demonstrating their robustness and effectiveness in challenging scenarios.

翻译：本文针对具有一般状态方程的狭义相对论磁流体力学（RMHD），发展了新型且稳健的任意高阶精度中心间断伽辽金（CDG）格式。该格式可被证明具有保界性（BP），即一致地保持亚光速流体速度的上界、密度与压强的正定性，同时（局部）维持磁场无散（DF）约束。在一维RMHD中，标准CDG方法严格无散，且其BP性质在可通过BP限制器实现的条件下得到证明。二维RMHD中，我们基于修正RMHD系统的适当离散，设计了可证明的BP且局部无散的CDG格式。其关键创新在于对修正RMHD方程中额外源项的离散，以精确抵消重叠网格上散度误差对BP性质的影响。我们给出了CDG格式BP性质的严格证明，并首次建立了RMHD中重叠网格上BP与离散DF性质的理论关联。由于原始变量关于守恒变量缺乏显式表达式，物理界约束呈强非线性，使得BP证明极具非平凡性。我们通过几何拟线性化（GQL）框架下的技术估计克服了这些挑战，将非线性约束转化为线性约束。此外，我们引入了一种新颖的二维重叠网格单元均值分解，该分解放宽了理论BP CFL（柯朗-弗里德里希斯-列维）条件并减少了内部节点数量，从而提升了二维BP CDG方法的效率。我们针对多种状态方程的广泛RMHD问题实施所提出的CDG格式，展示了其在挑战性场景中的稳健性与有效性。