Simulating general relativistic hydrodynamics (GRHD) presents challenges such as handling curved spacetime, achieving high-order shock-capturing accuracy, and preserving key physical constraints (positive density, pressure, and subluminal velocity) under nonlinear coupling. This paper introduces high-order, physical-constraint-preserving, oscillation-eliminating discontinuous Galerkin (PCP-OEDG) schemes with Harten-Lax-van Leer flux for GRHD. To suppress spurious oscillations near discontinuities, we incorporate a computationally efficient oscillation-eliminating (OE) procedure based on a linear damping equation, maintaining accuracy and avoiding complex characteristic decomposition. To enhance stability and robustness, we construct PCP schemes using the W-form of GRHD equations with Cholesky decomposition of the spatial metric, addressing the non-equivalence of admissible state sets in curved spacetime. We rigorously prove the PCP property of cell averages via technical estimates and the Geometric Quasi-Linearization (GQL) approach, which transforms nonlinear constraints into linear forms. Additionally, we present provably convergent PCP iterative algorithms for robust recovery of primitive variables, ensuring physical constraints are satisfied throughout. The PCP-OEDG method is validated through extensive tests, demonstrating its robustness, accuracy, and capability to handle extreme GRHD scenarios involving strong shocks, high Lorentz factors, and intense gravitational fields.

翻译：模拟广义相对论流体动力学（GRHD）面临诸多挑战，包括处理弯曲时空、实现高阶激波捕捉精度，以及在非线性耦合下保持关键物理约束（正密度、正压力及亚光速速度）。本文针对GRHD问题，提出了采用Harten-Lax-van Leer通量的高阶、物理约束保持、振荡消除间断伽辽金（PCP-OEDG）格式。为抑制间断附近的伪振荡，我们引入了一种基于线性阻尼方程、计算高效的振荡消除（OE）过程，该方法在保持精度的同时避免了复杂的特征分解。为增强稳定性和鲁棒性，我们利用GRHD方程的W形式及空间度规的Cholesky分解构建了PCP格式，解决了弯曲时空中可容许状态集不等价的问题。通过技术性估计及几何拟线性化（GQL）方法——该方法将非线性约束转化为线性形式——我们严格证明了单元平均值的PCP性质。此外，我们提出了可证明收敛的PCP迭代算法，用于鲁棒地恢复原始变量，确保物理约束在整个计算过程中得到满足。通过大量数值实验验证了PCP-OEDG方法的鲁棒性、精度及其处理极端GRHD场景（包括强激波、高洛伦兹因子和强引力场）的能力。